In finance, the Greeks are quantities representing the price sensitivity of derivatives (options in our case) to a change in an underlying parameter. Now that we know what goes into pricing an option, we can start deriving the derivatives of the price of an option in respect to each of
]]>In finance, the Greeks are quantities representing the price sensitivity of derivatives (options in our case) to a change in an underlying parameter. Now that we know what goes into pricing an option, we can start deriving the derivatives of the price of an option in respect to each of those underlying parameters. In this post, I'll go over broadly all the different Greeks we'll be looking at. In subsequent posts, I'll do a deeper dive with each.
Delta
This Greek is the measure of rate of change of an option's theoretical value with respect to changes in the underlying assets price.
Gamma
This Greek is the measure of the rate of change of the delta with respect to the changes in the underlying asset price.
Theta
This Greek is the measure of rate of change of the option's theoretical value with respect to the changes in time until maturity. Unlike other Greeks, where the variable can be unpredictable (underlying asset price can move up or down, volatility can go up or down, etc.), time can only move in one direction at a steady pace.
Rho
This Greek is the measure of rate of change of the option's theoretical value with respect to the risk-free interest rate. This is generally not dealt with on an individual basis but rather a team/group basis. When I was trading, the interest rates were so low and unchanging, that this Greek matter very little to us.
Vega
This Greek is the measure of rate of change of the option's theoretical value with respect to the volatility of the underlying asset. This one is probably one of the least understood by most people who trade. For my firm, given that we were options traders that didn't have an opinion on where the underlying was going to move to, vega is how we made most of our money, and I'll explain in detail later.
Etc.
As you can guess, there are a bunch more. The ones mentioned above are definitely the most commonly used (you can even look up these Greeks on Yahoo Finance) but the other ones are used more heavily by traders. These are generally second to third degree derivatives that give a more intimate understanding of the risks we face.
Extrinsic value (also called time value) is a little harder to understand. It's not something inherent in the option as it depends on a number of variables (time to expiration, strike price, perceived volatility). It is defined to be the premium a rational investor would pay over the intrinsic value
]]>Extrinsic value (also called time value) is a little harder to understand. It's not something inherent in the option as it depends on a number of variables (time to expiration, strike price, perceived volatility). It is defined to be the premium a rational investor would pay over the intrinsic value based on the probability it will increase in value before expiration.
This concept is quite hard to put in words and you might not fully understand it unless you see it in real life. But there are a few things I could tell you that might help you grasp the definition.
At the time of expiration, all extrinsic value goes to zero, since at expiration the option is worth its intrinsic value. If the option lands ITM (in-the-money) then it is worth something, but if it lands OTM (out-of-the-money) then it is worth nothing. There is no more time value left in the option.
Here is a graph that depicts the price of a 100 call option (depending on the underlying value) across different times.
There are two things to notice:
First, the value of the option is higher when there is more time to expiration. If you have a call option OTM by a little bit (e.g. $7 call when the underlying is worth $6), whatever that call option is worth to you 1 week from expiration (say $1), it would be worth much less a few minutes from expiration (maybe $0.05). Why? Because a lot can happen in a week but only so much can happen in a few minutes and it is in that expectation your time value decreases.
Second, the closer the strike price is to the underlying value, the higher the extrinsic value. In the graph above, the extrinsic values are the differences between the given line and the line at expiration. Graphing just the extrinsic values gives us the following:
So, with that, let's look at a few examples.
The underlying asset is trading at $7. The $8 call option just traded for $1.10. What is the extrinsic value?
Since we know an option value is just the summation of its extrinsic and intrinsic value. What is its intrinsic value? Well, a $8 call (with underlying at $7) is intrinsically worth nothing. That is, it is OTM. So, then ExtrinsicValue = $1.10 - $0.00 = $1.10.
Underlying is trading $34 and the $30 call just traded for $7.75. What is the extrinsic value for this call?
Again, what is the intrinsic value. Well, the call is ITM by $4. So, $7.75 - $4 = $3.75.
Let's try this for a put. Underlying is $101. $95 put option just trades for $6.50. What is the extrinsic value?
Well, the put has an intrinsic value of $6 ($101 - $95). So, the extrinsic value of $0.50.
This idea of extrinsic value will be further explored when we talk about the decaying time value of an option (theta). We might not explicitly call it out as an extrinsic value, but remember an intrinsic value of an option does not change in respect to time (only by changing the price of the underlying).
]]>Another way to look at the price of an option is to look at its intrinsic and extrinsic values. The price of an option is the sum of these two parts.
Let's talk about intrinsic value.
The intrinsic value is what the option is inherently worth. Or, in other words,
]]>Another way to look at the price of an option is to look at its intrinsic and extrinsic values. The price of an option is the sum of these two parts.
Let's talk about intrinsic value.
The intrinsic value is what the option is inherently worth. Or, in other words, the value of the option if it were exercised right now. It is also called exercise value. For instance, with corn prices being 4, the call option expiring in 3 weeks with a strike price of 3.75 has an intrinsic value of 0.25 (= 4.00 - 3.75). (If I exercise the 3.75 call option, I would be buying corn for 3.75 and can immediately sell it at 4 and profit 0.25). In another example, with corn price being 3.95, the put option expiring tomorrow with a strike price of 4.50 has an intrinsic value of 0.55 (= 4.50 - 3.95). (Notice how the time to expiration has nothing to do with an options intrinsic value).
Also note that an option can have zero intrinsic value. With oil prices being $50/barrel, a call option with the strike price of $60 has no intrinsic value (or an intrinsic value of zero). That is, why would I exercise the call option and buy a barrel of oil for $60 when I could just as well buy it for $50? Likewise, a put option with a strike lower than the underlying price would have no intrinsic value.
When an option has non-zero intrinsic value, we call that option in-the-money or ITM. So, if an option expires in the money, we would take care to exercise that option. As you probably guessed, an option with zero intrinsic value is called out-of-the-money or OTM. If an option expires out of the money, we would not exercise it.
Also slightly (un)related, if the strike price is on or near price of the underlying (i.e. underlying price is $51 and the strike price of the option under discussion is $50), we say the option is either at-the-money (ATM) or near-the-money.
A few posts ago, you saw the following graphs that represented the price of an option at the time of expiration. Since intrinsic value is the price of an option at expiration, the graph is an extremely useful tool to look at the intrinsic value of an option independent of time, volatility, or interest rate. The blue line is a call option with the strike of 15 and the orange line is a put option with a strike price of 35.
]]>So knowing the concept of expected value and fair price of a bet, we can start diving into pricing an option. As a quick reminder: options are contracts that give you the right but not the obligation to buy/sell the underlying at a predetermined price (known as the strike
]]>So knowing the concept of expected value and fair price of a bet, we can start diving into pricing an option. As a quick reminder: options are contracts that give you the right but not the obligation to buy/sell the underlying at a predetermined price (known as the strike price) on or before the expiration date. A call option will give you the right to buy and a put option will give you the right to sell.
We're not going to go into the mathematics of actually pricing an option (believe me, its complicated). Instead, we will look at the variables that are the input. In other words, we are going to look at the variables that change the expected value of outcome.
So, what variables might change the price of an option? Let's try to see what they are by looking at the definition of an option.
There are three more that are not explicitly stated in the definition:
With all these variables, we can specify which option we are talking about and estimate what the theoretical value of an option is. Using the theoretical value (the expected payout), if we buy it for cheaper than that and/or sell it for more than that, we are making a theoretical profit!
]]>Today, I'm going to talk about how to price options. I'm not going to do a deep dive but I will look at the different variables that go into pricing an option. In the past few posts, I mentioned we pay 2 or 3 for the option to buy/sell,
]]>Today, I'm going to talk about how to price options. I'm not going to do a deep dive but I will look at the different variables that go into pricing an option. In the past few posts, I mentioned we pay 2 or 3 for the option to buy/sell, how do we know what a fair price is?
Pricing an object, like a cup or a book, is relatively simple. There is the cost of creating the object (whether it is manufacture costs or labor costs) and a margin so the creator and seller can make a small profit. So, if it costs me $5 worth of materials to make a single shirt and it took me 3 hours of laboring (say I value my labor at $10/hour), then the total cost of creating a shirt is $35. I tack on some margin (say $7) and sell the shirt at $42. (This is oversimplified but the point is, it is easier to price a concrete object as opposed to a random event).
Before we get into pricing an option, we have to talk about how to fairly price something when the outcome is unknown (like an option, which, in essence, is a bet). We need to understand the concept of expected value.
What is expected value? The expected value is a probability-weighted average of all possible values. More intuitively, it is the long-run average value of repetitions of the experiment.
Let me share with you a simple interview questions often asked by trading firms to see if you understand the concept of expected value:
You and I are going to play a game of chance. You get to roll a fair six-sided die. Whatever result you get, I will give you that amount in dollars. For instance, you roll a 5, I will give you $5. How much are you willing to pay each time to play this game?
The real question that is being asked is: "What is the expected value of a fair die roll?" Or, in other words, if you were to roll this die infinitely many times, what would the average roll be?
Well, you have 1/6 chance of rolling each number, so the expected value is 3.5, as shown by the equation below:
It is worth noting that the expected value doesn't necessarily have to be one of the outcomes.
So, let's get back to the original question: "How much are you willing to pay each time to play this game?" Well, we now know that on average, the player will be earning $3.50 on each roll. So if you pay anything below $3.50 (say $3.49), you would eventually come out on top. The fair price of the game would be $3.50.
Let's look at another (slightly more complicated) interview question:
You and I are going to play another game. Much like the last game, you get to roll a die and you will get paid the amount you rolled. If you like your roll, that will be the payout, but if you don't like your first roll, you get to roll once more and have to keep the result. What is the fair price of this game?
So, we already know that the expected value of a die roll is 3.5, which means you would keep the first roll if it rolled 4, 5, or 6 (50% chance of happening and each roll (4, 5, 6) would have 1/3 chance of happening). In the other 50% (where you roll a 1, 2, or 3), you would roll the die again (which we already know has an expected value of 3.5). So, we can write this equation:
to arrive at the answer of 4.25
]]>So, we looked at buying calls and buying puts. Respectively, the graphs look like:
The blue graph is buying a call option with the strike price of 15 for a price of 2 (kink is at 15 and the most we can lose is 2). The orange graph is buying
]]>So, we looked at buying calls and buying puts. Respectively, the graphs look like:
The blue graph is buying a call option with the strike price of 15 for a price of 2 (kink is at 15 and the most we can lose is 2). The orange graph is buying a put option with the strike price of 35 for a price of 3 (kink is at 35 and the most we can lose is 3). We can also say (more simply) the graph on the left is for the 15 call for a price of 2 and the graph on the right is for the 35 put for a price of 3.
Let's take a look at selling calls and selling puts. I'll go into detail about selling puts (in my experience, this topic gives most people a hard time). Using the same put from above for this example (strike price of 35, the price of the contract being 3), let's say you are selling an option that gives the buyer the right to sell (to you) the underlying at the price of 35. What do you get in return for selling this right? 3! So, you collect 3 and you'll keep it if the price of the underlying , at expiration, is greater than or equal to 35 (since the holder of the put won't want to sell it to you at 35 when he can just go to the marketplace and sell it to someone else for more money). For any price under 35, he has the right to sell it to you at 35. For instance, if the underlying is valued at 28 at the time of expiration, then the holder might exercise his right and sell (to you) the underlying at the price of 35. That is to say, you have purchase the underlying from him for the price of 35 (even though you could buy it at the marketplace for 28). So, our graph will look a lot like the orange graph above, just flipped.
Okay. Now using the same logic for selling a call, we have the following graph:
In selling the put, the best case scenario is you collect 3. That is. There isn't anything better than that. The worst case, however, is when the underlying price goes to zero. You will be forced to buy the underlying (now worthless) for the strike price (35). So, the most you can lose is 35. Or, more generally, the strike price.
In selling the call, the best case scenario is your collecting 2. The worst case scenario happens when the underlying value goes up towards infinity. In that case, our losing is potentially infinite.
This is why most brokerage firms (Schwab, ETrade, Fidelity, etc.) won't let you sell options without making a very large deposit (called a margin) for those worst case scenarios.
]]>First, we'll look at general profit and loss graphs to make sure our audience understand basic algebra (Cartesian planes, slopes, intercepts, etc.). Then we'll take a brief look at futures. And finally, we'll touch on options.
So first, what does your PnL graph look like if you purchased a single
]]>First, we'll look at general profit and loss graphs to make sure our audience understand basic algebra (Cartesian planes, slopes, intercepts, etc.). Then we'll take a brief look at futures. And finally, we'll touch on options.
So first, what does your PnL graph look like if you purchased a single contract for the price of 34? If the contract was now worth 34, you would neither make anything or lose anything. If the contract was now worth 35, you would have gained 1. So on and so forth. Drawing this out, we get:
A couple of elementary things to note. First, note that the slope is 1 because we only purchased one contract. For each dollar the contract gains or loses, our PnL will be affected by that much. If we had purchased 3 contracts, then the slope would be 3 since if the contract gains a value of 1 (to become 35) we would have gained 3. Second, notice how much we could possible lose and how much we could possibly gain. If the contract value dropped to zero, the most we could lose is 34, whereas if the contract value went up towards infinity (that is, just kept rising) we could make an unlimited amount of money.
To drive the point home, let's look at selling 4 contracts at the price of 21. If the contract value goes up by 1, we would lose 4. If the contract value goes down by 3, we gain 12. Drawing it out, we get the following:
Don't let the graph fool you. The slope here is -4 since we sold four contracts. Again, what is our maximum loss and maximum gain? If the contract value drops to 0, then we stand to gain 21 * 4 = 84. If the contract value goes up towards infinity, we stand to lose and unlimited amount.
Now, let's consider drawing a graph for future contracts. Would it be much different from the graphs we have above? Not really (you'll see much different graphs soon when we start on options) because buying a future doesn't really give you protection against price movement. Sure, you get to lock in the price early on but if the underlying price moved, you would be susceptible to gain (or lose) purely on the market swings. So, how are options any different?
One thing to note before we get into options is that we pay a price for the right to buy/sell the underlying, whereas futures (and stocks) what you pay is what you get (that is, you can't just abandon a future or stock).
To draw the PnL of an option, we need to specify what option this will be. Without concerning ourselves with what the underlying contract (e.g. corn, oil, gold, etc.), we will just say the graph our PnL at the time of expiration if we were to own a 45 call option. I'll explain later why we specify such things as "at expiration."
Alright, remember what a call is? It is an option that gives us the right to buy at the strike price (which, in this case, is 45). So what happens if the underlying is price goes up to 50? In that case, we just exercise our option and we can buy the underlying (priced at 50) for only 45. In essence, we've just earned 5. On the other hand, if the underlying price drops to 40, we can simply abandon our option. In essence, we wouldn't have to lose anything. So, to summarize, here is our PnL graph:
A few things to note before we move on.
First, some people might ask, "why do we make nothing when the underlying price is equal to the strike price?" Well, if you think about it, you have the option to purchase something for 45 and its also worth 45... so your option is actually worthless. Any market participant has the right to purchase it for 45.
Second, notice that to the right of the kink (at the strike price of 45), the slope is 1. It is as if we own the underlying asset. That is not true when the underlying price is under the strike price, in which case, we don't care since at that point, we would rather abandon the call. (There are extremely rare situations when you would exercise a call where the strike price is higher than the underlying price, but we'll get into that later).
Unfortunately, this graph makes it look like buying calls is a risk free way of making money, since we don't have a loss. Actually, we did omit one vital piece of information: the price we paid to obtain that contract. In our example, let's say the price of the option is 2. That means, we should shift the graph down by 2 units to get the following graph:
Easy enough, right?
Now, consider this: what is the worst case scenario for buying a call option? What is the best case scenario? The worst case scenario is you lose the 2 units you paid purchase this call. The best case scenario is the underlying value shoots off into infinity and we make a killing! Limited downside and unlimited upside!
Now let's look at purchasing a put option. Again, without concerning ourselves with what the underlying contract (e.g. corn, oil, gold, etc.), we will just say the graph our PnL at the time of expiration if we were to own a 45 put option. Using the same logic as above (including actually paying for the put), we come up with this graph:
At the risk of sounding annoying, let me explain in detail what this graph is telling us. Owning the 45 Put gives us the right to sell the underlying at the price of 45. So, at expiration (the last day we have to use the option), if the underlying price is lower than 43, we make on the difference. For instance, if the underlying price is 39, then we can sell it at the price of 45 and (in essence) purchase it back for 39; we would have made 45 - 39 = 6 from the option, less the 2 we paid to obtain the option (total profit is 4). On the other hand, if the underlying price is higher than 45 (like 51), we can sell it at the higher price (of 51) instead of the option's strike price of 45. So, we just abandon the contract, losing the initial amount we paid to get the option.
Okay, we just looked buying calls and puts. Next time, we'll look at selling calls and selling puts.
]]>Finally, options! This was my bread and butter. As part of my firm, I was an options market maker, that is, I provided liquidity (competitive bids and offers) in the options market. This role was partially possible given the extensive understanding of options and their risks hammered into us via
]]>Finally, options! This was my bread and butter. As part of my firm, I was an options market maker, that is, I provided liquidity (competitive bids and offers) in the options market. This role was partially possible given the extensive understanding of options and their risks hammered into us via the strict training we received.
So, what are options?
They're a lot like futures in that it is a promise (or a contract) made for a future delivery date. Unlike a future, in an option, you have the option (or choice) to exercise it or not. The fact that its a contract also means that you can sell one without actually owning one (much like a future contract). Keeping these in mind, let's look at the formal definition.
An option is the right (but not the obligation) to buy or sell the underlying asset at a specified price on or before a certain date. A call option gives the holder the right to buy the underlying asset; a put option gives the holder the right to sell the underlying asset.
Let's look at an example to drive this definition home. Then we'll look at and define the different parts of an option.
Bob works for Kellogg Cereal where it is his job to purchase the necessary corn to make cereal. To reduce his risk, he purchases a call option for $3,000 that gives him the right but not the obligation to purchase 10,000 bushels of corn for $4.00 a bushel on or before November 1st, 2010. On November 1st, 2010, if corn prices are lower than $4.00, Bob can go to the market and just purchase it for a cheaper price and allow the option to expire. If, however, corn is more expensive than $4.00, Bob can exercise his option and purchase the corn for $4.00 (cheaper than it is to buy it in the market).
Alright, let me define the different parts:
Still a bit confused? I'm going to give you a few examples to hammer it in. In each example, I will point out all the different parts of the option (buyer, seller, expiration date, etc.).
It can be a bit confusing as there are a lot of moving parts. Here's a word of advice: do not get the actual price of the option mixed with the strike price. The actual price is the value of the option contract, while the strike price is a part of the options contract that specifies at what price I can later buy/sell the underlying asset.
I hope this post made some sense. You probably won't understand completely until we see a few more examples. In the next post, we'll look into some simple PnL (profit and loss) graphs to show the potential winnings and losses of an options contract.
]]>Given the nature of my job as a trader, it was of utmost importance to know everything about the product you were trading. As such, the details for the examples provided in this blog post can be a little bit daunting. To further complicate things, there might be some words
]]>Given the nature of my job as a trader, it was of utmost importance to know everything about the product you were trading. As such, the details for the examples provided in this blog post can be a little bit daunting. To further complicate things, there might be some words and phrases I haven't explained yet, but that's because I can't talk about one aspect of a futures contract without bringing up another. I'll try my best to explain everything clearly. Let's get started.
We'll take a look at two examples: Corn Futures and S&P 500 Futures.
Corn futures are traded at the Chicago Mercantile Exchange (formally Chicago Board of Trade) under the symbol ZC. You can see a summary of the contract specs at this website (this pdf file is the actual rulebook). As you can see, everything (from the size of the contract to when/where it will be delivered) about the contract is standardized and specified.
First, note the contract size. Contract Multiplier (or contract size) is the amount of underlying asset each contract represents. In this case, for each corn future you purchase, you are purchasing a future delivery of 5,000 bushels of corn delivered to one of the locations mentioned in the rulebook (you have to arrange to pick it up yourself).
The pricing unit is "cents per bushel." For instance, if the purchase one corn future contract for a price of 400, I would be paying 400 (cents / bushel) * 5,000 (bushels) = 2,000,000 cents (or $20,000) in cash. (While the official prices are printed as such (400 or 401), traders will often prefer to look at it as dollars and not cents. So you can think 4.00 (dollars / bushel) 5,000 (bushels) = $20,000 instead).
Now that we know how it's priced, let's take a look at the tick size. The contract specs say it ticks in "1/4 of one cent per bushel." So, if you have a price of 3.45 the next increment of price would be 3.4525, then 3.4550, then 3.4575. On the exchange, the prices are represented in eighths (because the corresponding option contracts tick in eighths), even though it ticks in quarters. For instance, you might see the last price traded as 375'4 (which would equal 3.7525, equivalent to 3.7525 * 5,000 = $18,762.50).
Finally, the contract specs indicate how these corn futures are settled. Settlement is the act of executing the contract when they expire and can be done in one of two ways. Physical delivery is when the amount specified of the underlying asset is delivered by the seller to the buy. Cash Settlement is a cash payment made based on the loss/gain related to the contract.
S&P 500 Futures are also traded on Chicago Mercantile Exchange (CME) under two symbols SP (the "Big") and ES (the "Mini"). These futures are based on Standards and Poor's 500 (an American stock market index that best represents the U.S. stock market). Why the two symbols? It's because they have two different multipliers. We'll see shortly why these details matter so much in a trader's world.
The "Big" contract is traded in the Open Outcry trading pit at the CBOT pit during regular trading hours. When the floor (or trading pit) closes, it moves onto CME's electronic platform called CME Globex. The "Mini" contract trades exclusively on CME Globex.
The contract sizes for the "Big" is $250 * the S&P500 and trades in $0.10 ticks. So each tick is worth $250 * 0.10 = $25. For instance, if you purchased one of the SP contracts for 1895.20 and sold it one tick up at 1895.30, you would have just made exactly $25 (minus any transaction fees).
The "Mini" contract is 1/5th the size of the "Big" at $50 * the S&P500. The smallest increment (one tick) is $0.25 and so 1 tick equals $50 * 0.25 = $12.50. Notice how even though the ES tick size is larger than the SP (0.25 versus 0.1), because of the contract size the actual increment in dollars is smaller. The E-mini is usually the vehicle of choice for most traders given its accessibility (electronic), smaller size (contract size) and liquidity (more people trade it).
Finally, both SP and ES are cash settled. For instance, let's say I purchased one ES for the price of 1807.25. The monetary value of my investment would be 1807.25 * 50 = $90,362.50. On the day of expiry, the S&P index settles at 1809.32. Then since I purchased the future, I would have made 1809.32 - 1807.25 = 2.07 points (monetary value of 2.07 * 50 = $103.50). In another example, let's say I sold a SP contract at 1825.40. On the day of expiry, let's say the index settles at 1835.20. I would have lost (1835.20 - 1825.40) * 250 = $2,450.
S&P500 is of particular interest to options traders across the US (most of them in Chicago), given its liquidity and potential earnings. We'll definitely come back to discuss trading the S&P500 in the future.
(Note: Now that you know what contract specs are, I won't necessarily put dollar signs for prices. That is, if I say I buy an option for 3.00, it means just that. The cash value of 3.00 varies greatly depending on the contract size and multiplier.)
I did a similar exercise for Bitcoin Futures when they first released it a few months ago. Check it out here.
]]>There are a lot of variables to consider when we are talking about pricing a forward/future. For now, we'll simplify the problem and focus on the few key variables: the risk-free interest rate, the time until delivery date, and the underlying price.
Since in a forward/future contract, we
]]>There are a lot of variables to consider when we are talking about pricing a forward/future. For now, we'll simplify the problem and focus on the few key variables: the risk-free interest rate, the time until delivery date, and the underlying price.
Since in a forward/future contract, we are agreeing to pay the amount of money on the day of delivery, we need to take into account how much the money is worth when the trade actually happens. For instance, you have $1,000 right now but the future contract says the actual exchange of cash and goods will happen exactly 250 days from today. How much is that money worth to you at the time the exchange?
To answer this question, let's look at r -- the risk-free interest rate per year. If you deposited some money into a bank account, you might notice the bank will pay out some sort of interest rate on your cash (nowadays, the interest rate is extremely low but that's a whole other discussion). This observation also presents a small problem since when the bank pays the interest is important to how much money you will be making off the interest. Let me show you in some concrete numbers.
Assuming the risk-free rate of interest per year, r, is 3.25%, what is $7,000 today worth in 5 years?
First, let's assume the bank pays the interest once a year. So after the first year, the bank pays 3.25% interest on $7,000 (which is $7,000 * 0.0325 = $227.50), making your total amount $7,227.50. After one more year, the bank pays 3.25% interest on what you currently have in your bank ($7,227.50) which makes the total $7,462.39 [ = $7,227.50 + ($7,227.50 * 0.0325) = $7,227.50 * (1 + 0.0325)]. We can simply the equation into the following:
But what if the bank -- instead of paying every year -- pays every 6 months? Or every month? Or every day?
We can drill this down into smaller and smaller increments (think every minute, every second, every half a second, etc.). If we take continue down this road, we assume that the interest is paid continuously. Then (maybe you remember from high school algebra) we will approach e (Euler's Number). That is:
So, to summarize, we can say that
where r is the risk-free interest rate per year and t is the time in terms of year. So, to answer the previous question (you have $1,000 right now but the future contract says the actual exchange of cash and goods will happen exactly 250 days from today. How much is that money worth to you at the time the exchange?), we have the following:
So, how does this math translate into calculating the price of a future contract? Well, under the simple assumptions we put in place, your future contract will be worth what the underlying asset is worth times the interest that your money will accrue until the time of the exchange.
For example, in Andy and Steve enter into a forward contract. Andy promises to pay Steve to pay some amount of money in exactly 500 days and Steve agrees to give Andy 5,000 bushels of corn in 500 days. The 5,000 bushels of corn is currently worth $20,000. If the risk-free interest rate is 4.25%, what is the fair price Andy should promise to pay Steve?
Note that just because you entered into a forward/future contract, you are not immune to the moving prices. In fact, under the assumptions (and generally true) you are just as open to price movement risk as much as the guy who is currently holding onto the underlying asset. If the price of corn were to move up, you would profit from it (since in essence you bought it at a determined price in the future), whereas if the price went down you would lose.
The equation becomes more complicated when you start to consider the cost of carry (e.g. if you promised to sell me 50 barrels of oil in 5 months, where are you going to store it until then? Surely, you can't be doing that for free), any future income stream, or (if we're talking about stocks) any future dividends.
For the most part, in my job, we did not price futures, which is one of the reasons I'm sort of skimming this part. Instead, we focused mainly on pricing options that were based off of futures. To price the futures, we simply used the bids and offers that were available in the market. There are, however, traders that trade the spread between price of the underlying asset and the price of the future.
]]>My wife and I spent a few days in Budapest this past month. I wasn't quite sure what to expect from Hungary but by the end
Hungarians were nomads from the eastern part of the Ural Mountains (deep in current day Russia) who settled on the
]]>My wife and I spent a few days in Budapest this past month. I wasn't quite sure what to expect from Hungary but by the end
Hungarians were nomads from the eastern part of the Ural Mountains (deep in current day Russia) who settled on the Hungarian steps around 895 AD. Legend has it that the leader of the Hungarian tribes had a dream in which eagles were attacking their horses but a Turual came to save to them. This dream symbolized that they had to migrate. When they did, the Turul led the nomads to the land that eventually became Hungary.
In 1000 AD, Saint Stephen (aka King Stephen) founded the state of Hungary and accepted the Catholic religion. They were one of the latest European nations to adopt Catholiscism. And then from then WWI, Hungary was pretty much the victim of a lot of invasions starting with the Mongols to the Turks and then finally the Hapsburg.
In the first world war, Hungary was an ally to Germany and Austria. Then they allied with Germany in the second world war only to switch to the Soviets when they say the writing on the wall. The communist rule lasted until 1898 when Hungary finally became an independent democracy.
My wife and I spent about 6 days in Budapest for a conference. We both worked for half that time, which gave us 3 days to enjoy the city. Given the history of the city/country, it wasn't surprising to see that there wasn't a whole lot to do, but here is a list of things we did.
Budapest sits on a patchwork of thermal springs. That combined with the Turkish influences gives Budapest its famous thermal baths. We spent an afternoon at the Gellert Baths, a part of Budapest's luxarious Gellert Hotel.
First thing to note is that despite the term bath, everyone is required to wear swimsuits as all the baths and saunas are not segregated by sex. ALso, while not required, I would suggest you bring a pair of flip-flops for walking between the different pools.
There were 7 baths located throughout the building that we wandered around in. The coolest bath was a cool 36 degree celcius and the hottest was at 42 degrees celcius. The coolest part is the art nouvaeu style the bathouse was built in. It definitely felt like you were swimming in a cathedral!
Overall, I was bit underwhelmed because I kept comparing these baths and saunas to what I was used to (the Korean equivalent -- Jjimjilbang).
Castle Hill is a great area on the Buda side of the city and hosts a number of sights that you wouldn't typically find in a European city.
There is the Matthias Church which was built in 1505 (it was destroyed by the Mongols in 1241 and then built again). While it is a Catholic church, it has clear Islamic influences in his architecture.
Directly next to the Matthias Church is the Fisherman's Bastion which was built in 1895 (finished in 1902). The seven towers you can see represent the seven Magyar tribes that settled in the Carpathian Basin in 895.
The House of Terror is a memorial to the victims of the communist and facist regime of the 20th century. The exterior was built to stand out on the main street in Budapest as it stands as a stark reminder of Budapest's past. It should also be noted that the building was used by the Arrow Cross Party, Hungarian Secret Police, and the Nazi party leading up to and following World War II.
Inside we saw exhibitions detailing the persecution by first the Nazi regime and then the Soviet regime. It starts on the third floor with the Nazi regime and the Arrow Cross Party and we made our way down through the second floor where they covered the Hungarian Secret Police. The exhibition ends in the basement where they kept the cells that were used to hold and break prisoners during the communist regime.
Throughout the museum, there is an abundant amount of information in video footage of interviews with Hungarian people. Also throughout the rooms, we saw printouts of extra information detailing the history in depth. The only downside was there was a lot of reading and no sitting room, so make sure you wear comfortable shoes when you visit!
One of the coolest part of Budapest was its nightlife in the Ruin Bars. These bars were started in the historic Jewish Quarter. When the buildings were deemed too unsafe to live in, a couple entrepeuners set up a bar in an abandoned factory that was set for the wrecking ball. Since then the popularity has spread rapidly and the entire Jewish District comes to life at night.
]]>In the past few months, we've talked about fundamental vocabulary, the idea of trading, making markets, retreating, and the different markets that exist. With the fundamentals of trading out of the way, let's dig into some of the slightly more complicated concepts: forwards and futures.
A forward contract (or simply
]]>In the past few months, we've talked about fundamental vocabulary, the idea of trading, making markets, retreating, and the different markets that exist. With the fundamentals of trading out of the way, let's dig into some of the slightly more complicated concepts: forwards and futures.
A forward contract (or simply forward) is a contract between two parties to buy or sell an asset at a specified time in the future for a priced agreed upon today.
An subset of forward contracts is futures contracts. A futures contract (or simply future) is exactly the same thing as a forward, except it is standardized, regulated, and traded on an exchange.
Here's an example of a forward contract. I'll give you $5 tomorrow if you give me a cup of coffee tomorrow morning -- Here, the two parties would be you and me; the contract is for me to give you $5 (the price agreed upon today) so I can receive a cup of coffee from you tomorrow (specified time in the future). In this context, you would be the seller of the forward contract since you received a predetermined price (money) and promised to deliver at a later date, and I would be the buyer. You and I can hash out the details of what type of coffee, where the delivery will take place, and more.
Whether you're aware or not, large banks will trade with each other in a similar manner, buying and selling financial instruments (commodities, currencies, risk) "over-the-counter" without any supervision of an exchange.
With a futures contract, all the details are already hashed out by the exchange. The exchange publishes these standards and calls them contract specifications
There are some clear advantages and disadvantages of trading "over-the-counter" versus trading on an exchange.
If a stranger came up to you and asked you to buy a corn forward from him (you promise to pay him $4 dollars in a month and he promises to give you a bushel of corn also in a month), you probably wouldn't take him up for the trade. Most likely, you would avoid this trade because there is too much risk in trusting a stranger with a promise to deliver. This is called counter-party risk and has to be considered when trading over-the-counter.
When you trade on an exchange, you are actually trading with the exchange. That is, if you went to the CBOT and purchased one corn future contract at the same time someone sold one corn future contract, you wouldn't be buying the contract from the seller but from the exchange. This virtually eliminates counter-party risk.
Another difference stems from the regulations on standardized contract specifications. At an exchange, you know exactly what you are getting, but you can't tailor the contract in any way to suit your needs. On the other hand, on OTC markets the flexibility can pose problems of its own; since not everyone knows what you are trying to buy/sell (it's not standardized), less parties are ready to trade (the party will spend time and resources to understand the new risks involved with a new contract). Whereas with a standardized contract, all parties involved know the risks beforehand.
In the next post, I plan on discussing how we determine the price of a future contract. Then we'll dig a little deeper with a couple of examples of contract specs and discuss some more important concepts that are crucial in understanding futures (and eventually options).
]]>With the recent rise of popularity in investing in cryptocurrency, I wanted to write a post about the dangers the lack of regulations in an exchange.
While we are seeing a move by the world governments to start to identify crypto-trading as an investment (thereby demanding folks pay a capital
]]>With the recent rise of popularity in investing in cryptocurrency, I wanted to write a post about the dangers the lack of regulations in an exchange.
While we are seeing a move by the world governments to start to identify crypto-trading as an investment (thereby demanding folks pay a capital gains tax on your profit), we have yet to see governing authories (at least in the US) start to crack down on the exchanges (and ICOs) with regulations.
Prior to the infamous Black Tuesday, the only laws in place to protect investors from worthless securities were on the state level and were known as the blue sky law. The first blue sky law was enacted in Kasas in 1911 and quickly expaned into 47 states by 1933. These state securitie laws were named for the evil at which the law aimed such as "speculative schemes which have no more basis than so many feet of 'blue sky.'" These laws required companies to disclose how much interest they were getting but didn't stop the investors from buying (as long as they were "informed"). Further, these blue sky laws were ignored when companies were making securities offering across state lines.
In response to the Great Depression, we see FDR's New Deal enacted. Congress passes the Securities Act of 1933 which regulates the interstate sales of securities at the federal level. A year later, with the passage of the Securities Exchange Act of 1934, the Securities and Exchange Commision is created to enforce the federal securities laws.
Since the 1930's, Congress has continued to empower the SEC hoping to make the market a safer place for an individual investor.
Here is a list of examples of market manipulation you will see in any typical crypto exchange. As you can tell from the examples below, it is incredibly hard to prove the intent behind these manipulation, but at lest you'll have a frame of reference when you see a flurry of activities in the market place.
Wash Trades — where you trade with yourself, to pump the price up or down, or just create the illusion of trading volume. You could literally do this in the Bitfinex trading engine quite recently.
Spoofing — where you place a large order to create the illusion of market optimism or pessimism, and cancel as soon as the price gets anywhere near it. This can be seen quite often on Bitfinex and Coinbase/GDAX.
Painting the Tape — like wash trading, but with two or more participants. Mark Karpelès admitted in court that he had been using the “Willybot” to pump up the Bitcoin price on the Mt. Gox exchange during the 2013 Bitcoin bubble.
Front-Running — where a market participant takes advantage of a buy or sell order before other customers can. Typically folks in high-frequency trading get a lot of heat for this but it's improbable outside folks in crypto are taking advantage of the markets. Instead we are seeing insiders with access to the database trading on their own exchange — Bitfinex officers trade on the exchange themselves. They state that they avoid conflicts of interest, but there is no oversight or transparency on this.
Pump and Dump / Trash and Cash - where a group of market participants artificially increase/decrease the price through rumors. We see this quite often in a variety of alt-coins where there are no significant announcements/news and yet the prices go up 200-300% and drop as quickly in a day or two. I have read (but not confirmed) there are discords channels out there for this specific purpose.
Quote Stuffing - flooding the market with large quantities of orders and gaining an advantage over slower market participants
Now that you know of these manipulations, just be wary of them. These won't stop until there are more regulation (or people start boycotting one exchange over another) and I don't see that happening in the near future. At least now you are aware and can stay safe while trading!
Edit: I just came across this article that also talks about price manipulations in Bitcoin when Mt. Gox was still alive.
Edit2: Also, this is a great article of finding a bot that painted the tape.
]]>On the exchanges where I traded, there are mainly two types of trading. One takes place on the floor (in the pit, downstairs, open outcry, etc.) and another takes place on the screens (electronic trading, upstairs, etc.).
Let's start with trading "in the pit" (officially
]]>On the exchanges where I traded, there are mainly two types of trading. One takes place on the floor (in the pit, downstairs, open outcry, etc.) and another takes place on the screens (electronic trading, upstairs, etc.).
Let's start with trading "in the pit" (officially known as open outcry). Before computers and the internet, exchanges would have trading floors where registered traders could come and buy and sell contracts. The trading floor was divided into many different sections: there would be specific locations to trade (the trading pit), another section to record and reconcile trades, and yet another to take phone calls from your clients. In the 1990's, these trading floors slowly became obsolete with the advent of computers and electronic markets. There are still small pockets of pit trading around today.
Trading on the floor is its own little world. Imagine standing in a group of people, elbow to elbow. A guy with a piece of paper walks in and asks the crowd "My client is looking to buy 50 oil future contracts! Offers?" This question sparks a frenzy among the traders trying to deliver the best price the customer can buy oil for. "I can sell you 30 at 81!" "I have 50 at 80." "10 at 79!" The customer waits a few seconds for the best price. It seems no one can sell it below 79, so everyone is now calling out sizes at 79: "5 at 79" "10 at 79" "15 at 79" "10 at 79!" Meanwhile everyone has their hand up to signal their sizes and their prices. The guy looks around and points to 2 guys and says "I'll buy 10 from each of you," writes on a piece of paper and walks away. The two guys who just sold contracts are also hurriedly writing down the information so they can hand it to their clerks who will enter it into the system.
Now let's imagine trading on the screen. You are sitting behind multiple computer screens; on one screen, you see all the trades that are going through the market and a list of all the trades you've made today. On another screen you're looking at the parameters you use to control the theoretical (or perceived) value of the instruments you are trading. On the main screen you have a list of all the instruments you are trading with a bid price and a bid size on the left and an offer price and offer size on its right. The numbers are constantly changing as people put in and take out bids and offers. Your electronic eye (or automatic trader) looks out for any opportunity to trade based on your parameters (for instance, if the computer sees a chance to buy anything for 25 cents less than its theoretical value, purchase it and notify the user). You sit behind the computer, looking for any opportunities to make a good trade (much like a trader in the pit would be standing around looking/waiting for a good opportunity to trade). However, unlike trading on the floor, the computer looks for opportunity much faster than a human brain can process all the information, and before you know it, your computer makes a sound and a trade appears on your trade list: you've just made a trade!
Speed. Trading electronically means you can let the computer do the heavy lifting in terms of calculating simple profit and loss to evaluating how much risk is associated with the trade; all the arithmetic you had to complete in your head, the computer can do that in a fraction of a second. On the other hand, given the computer's speed and complexity, mistakes can happen before it can be stopped and mistakes can be often overlooked given the number of things that are happening at any given moment.
Counter Party Evaluation. When you're on the floor, you almost always know who you are doing the trade with. Who just purchased 200 shares of IBM stock? Who did he buy them from? These are all questions that can be answered as long as you are aware of what is going on. And using the information on who bought and who sold, you can make inferences about what trades might happen next. However, on the screen, you are not given that information. All you know is that 200 shares of IBM stock traded at a certain price. You have no idea whether it was Goldman Sachs that purchased it (and therefore might be an indication of a bigger trade coming your way) or if it was an individual investor.
The best analogy I've heard between trading on the floor and on the screen is like playing poker at the casino or over the internet. In the casino, you see who you're playing against. You can see their reactions, you can see if they leave the table and come back to sit at another seat. If you play poker over the internet, you might have more analytical tools at your disposal (e.g. percentage of pre-flop folds, etc.) given the amount of number-crunching your computer can do; however, each player hides behind their username. You can't see their reaction, who they're looking at, or even how much alcohol they've consumed.
Most of the trading activity are slowly migrating to the screens, eliminating the inefficient transactions that happen with yelling and gesturing (that's a whole other topic I'll write about in the future). However, some trades still go through the floor, and it would be irresponsible for a trader to completely ignore one side.
When I was trading, depending on what market you were involved in (equity, foreign exchange, metals, energy, interest rate, etc.), roughly 70% of the trading volume were going through the screen.
]]>Continuing from the previous post about market makers, let's look at an example.
Let's set the scenario. Let's say this mystery contract ticks in nickels (0.05) and I always want an edge of 0.12. Also, I am willing to do 10 lots (contracts) at a time. Finally, our
]]>Continuing from the previous post about market makers, let's look at an example.
Let's set the scenario. Let's say this mystery contract ticks in nickels (0.05) and I always want an edge of 0.12. Also, I am willing to do 10 lots (contracts) at a time. Finally, our algorithms tell us that the contract is worth 6.00. So, what is our bid and what is our offer?
Since we want at least 0.12 edge, the best bid we can put in is 5.85 bid (since 6.00 - 0.12 = 5.88, but it ticks in 0.05, so the highest I can go is 5.85). Likewise, we want 0.12 edge on our offer as well, so our offer would be 6.15 (again, 6.00 + 0.12= 6.12, but it ticks in 0.05). So, we are 5.85 at 6.15, 10 up. And to make it easier, we can show:
Great. So, we show our market in the exchange and we wait.
A buyer comes into the market and is looking to buy 7 lots. We show him our offer and he decides he can pay 6.15. Since we are only comfortable doing 10 lots at a time and we already did 7 on the offer, we now have 3 left on the offer. So, our market (bid-ask spread) looks like the following:
Let's continue. Another buyer comes in and buys the remaining 3 lots we have sitting on our offer. That means, we have no more lots to offer at 6.15. Now, we "retreat."
What is retreating? Retreating^{[1]} is the consequence of updating the perceived value (theoretical price) of the instrument.. In doing so, you will set up a new market (bid-ask spread) that will biased into flattening out your position. For instance, the more you buy a contract, the less it becomes worth to you (and likewise, the more you sell something, the more it will become worth to you). In treating the value as such, you will become more and more aggressive to exit your position. Let us revisit the above scenario to drive the point home.
Let's say we retreat 3 cents. Like I said before, since we sold, we increase the value of the instrument. Then the new theoretical price will read 6.03. Since I am always seeking at least 12 cents in edge, my bid will now be 5.90 (6.03 - 0.12 = 5.91). Further, my offer will be 60.15 (6.03 + 0.12 = 6.15). So my market would look like the following:
There are a couple of things to notice. First, notice that we didn't retreat our offer. We are still at 6.15 (still have an offer at 6.15). But, notice our bid, its moved up from 5.85 to 5.90. We are more aggressive to buy back our short position. And the more aggressive we get, the more likely our bid will be filled.
Something else to note is that the amount we retreat will reflect our appetite for risk. In the previous example, we simply retreated 3 cents. That means, we would have to retreat 4 times (12 cents of edge / 3 cents to retreat = 4) for our initial trade to be an even trade (no profit). Let's take another look at the example but set a different retreat amount.
This time, let's say we retreat 5 cents. Using the same logic as before (theoretical value goes up 5 cents and we recalculate our market), we get the following:
What if we retreated 8 cents? We would get the following:
Keep in mind that all the retreat examples we looked at were smaller than the edge we ask for. Imagine if we retreated 50 cents (when we only asked for 12 cents). We would be doing trades left and right, but we would be giving away free money! We would be buying it expensive and selling it at a steep discount.
Retreating is an essential part of market making. In doing so, you are more likely to get out of your current position and less likely to expand on it. In our example, we sold 10 lots, and as we continue to retreat our bids got more aggressive to buy back our sold contracts and our offers became less competitive as we backed away from our initial price. Again, the amount we retreated determined how aggressive we were trying to get out of our position.
The actual retreating can be done in (mainly) two different ways. First, you can change your theoretical price to reflect what the new value is. Second, you can change the amount of edge you ask for. I personally believe the former is the way to go, as the latter method proves to be not only cumbersome but deceptive of what you truly believe the value of the contract is. ↩︎