Options. In English [Part 2]

I wrote the first installment of this series over two years ago, promising to explain the practical ramifications of the the basics that I’d covered using the tools of the trade. After enough procrastinating, I’ve finally gotten around to doing the second installment.

Questions Answered

Before I begin I wanted to address a number of questions that were emailed to me between my last options article and this posting. If you have any other questions, shoot me an email. justin [dot] braun [at] scaleddynamics [dot] com.

Q: What are some different risk management styles?  Especially ones that would make options more attractive than futures.

Managing risk is ultimately looking at your trading strategy and asking “what can go wrong?”

A popular strategy for day traders is to make sure that they go home flat (not have a position on) every night. Historically, this would limit the amount of money they can lose by avoiding price gaps between sessions. Many exchanges place daily price floors and ceilings on how far a tradeable instrument can move from its opening price (or in some cases, previous day settles) in a day. Further, the less time you have a position on, the less opportunity you have to lose money. High frequency traders take this to the extreme, trying to hedge or even take profit from a trade microseconds after a position is put on. Options are significantly less liquid and with the exception of trading deeps against futures, exiting positions every day would require the trader to give up an unrealistic amount of edge.

If you’re long options, these limits are built into how little the option can decrease in value. Buying a combination of puts and calls will typically yield a long volatility position. With a long volatility position you will lose money in the form of theta decay every day as the time value of the position diminishes, but make money during large price moves or during increases in volatility. The advantage of such trades are that your capital-at-risk is roughly equivalent to the price of the options you purchased, and watching your erosion is a daily expected occurrence.

If you’re short options, time is literally on your side in the sense that you collected a cash premium for something that will diminish in value every day….. or go in the money and cost you a fortune. Writing premium (or selling calls and/or puts) is a very risky  proposition, but it will pay you consistently… until it doesn’t.

Q: How important is it to know the actual math behind the greeks? 

Not at all!! If I were asked to explain the math that goes into any of the models I write about, I’d be immediately exposed as a quack! I can only add, subtract, multiply, and, on a good day, divide. With that said, my customers can attribute millions of dollars of profit to the systems I’ve built. What is important is a qualitative understanding of the meaning behind each greek and how a given action (getting a fill, change in underlying, change in volatility,passing of time, change in interest rates) will change your position and exposure.

Q: How is Implied Volatility calculated?

Most options models use a partial differential equation to calculate their values, meaning that the equations are unidirectional. You can’t get the inputs from the result. Since volatility is an input, you need to take a guess what the volatility is most likely to be, and then search for the correct value by moving inputs up and down until you get the right value. This is very computationally expensive, but not as bad as it sounds. The Newton Rhapson method is the most commonly used way to search for the correct values in an efficient manner.

In practice the better your first guess is, the smaller a net the algorithm has to cast to search for the proper value. You might search for a known volatility of a nearby strike, or a previously known volatility, for example.

Setting up a Trade

From the beginning, the power of options are that they give you significantly more control over how much exposure you wish to obtain, and they allow you to make bets on more than just direction. Unlike futures, fair value is stupid-easy to calculate. You choose an underlying instrument, pick a pricing model, and voila, you have fair-value. None of the nuances of the multitude of models out there matters close to expiry and/or near-the-money. While nothing stops you from having one and trading based on it, an opinion about whether the underlying market will go up or down isn’t necessary.

To that point, say that you have no clue whether the price of gold is going to go up or down, but you do think that the market is a bit too quiet compared to other commodities. You think that regardless of what happens, gold is in for a big change in price, but you’re not sure what direction it’s going to move. The trade: Buy Straddles or Strangles.

A Straddle is the buying of a call and put at the same strike price, and a Strangle is the buying of a call and put at different strike prices. The difference is that the capital at risk of a strangle is a fraction of that of a straddle, and the comparative payout is larger as well.

As of this writing, gold is trading at around 1465. The June 1465 calls and puts are trading around roughly 35 at approximately 21.3% volatility. Let’s plug this into the formula engine inside of SD Gatekeeper and simulate what a straddle trade might look like.

Formula Audit

First let me explain how my formula engine works. Each function outputs the result of a calculation with various arguments. I can either use static values for arguments, or pull directly from an instrument feed. In this example, I am doing a combination of both, pulling the strike price and expiration date directly from the Jun13 1465C instrument, and setting the futures (underlying), interest rate, and volatility manually. Using the same inputs, the following formulas produce the following values:

B76.Price.Call(Future: 1465, Strike: Primary.Strike, Rate: Rate, Time: Primary.YearsToExpiry, Volatility: Volatility) = 35.36

B76.Price.Put(Future: 1465, Strike: Primary.Strike, Rate: Rate, Time: Primary.YearsToExpiry, Volatility: Volatility) = 35.36

B76.Price.Call(Future: 1470, Strike: Primary.Strike, Rate: Rate, Time: Primary.YearsToExpiry, Volatility: Volatility) = 37.97

B76.Price.Put(Future: 1470, Strike: Primary.Strike, Rate: Rate, Time: Primary.YearsToExpiry, Volatility: Volatility) = 32.98

(38+33) - (35.4 + 35.4 ) = .2

 

Assuming that you could buy both put and calls at 35.4 (gold options tick in .1) when the futures were at 1465, and assuming that you could sell them at 38 and 33, you’d have locked in a profit of .2 (or 2 price increments) on a $5 price move in the underlying.

Now let’s see what that same move would look like with a Straddle. This time we’ll buy a call and put that are $5 out of the money.

B76.Price.Call(Future: 1465, Strike: 1470, Rate: Rate, Time: Primary.YearsToExpiry, Volatility: Volatility) = 32.98

B76.Price.Put(Future: 1465, Strike: 1460, Rate: Rate, Time: Primary.YearsToExpiry, Volatility: Volatility) = 32.86

B76.Price.Call(Future: 1470, Strike: 1470, Rate: Rate, Time: Primary.YearsToExpiry, Volatility: Volatility) = 35.48

B76.Price.Put(Future: 1470, Strike: 1460, Rate: Rate, Time: Primary.YearsToExpiry, Volatility: Volatility) = 30.56

(35.5+30.6)-(33+32.9) = .2

In both cases, a profit of .2 was locked in however the picture is not so simple. First, the strangle position cost less to purchase (70.8 vs 65.9) so the returns of the straddle are larger. Further, in the example shown I was using a flat volatility of 21.3%. In real life, volatility changes from strike-to-strike. When viewed on a graph, volatility tends to have a specific shape.

VolEdit

The green line in the middle represents where implied volatility is at each strike. Note that the line slopes slightly down to the right (higher strikes). This means that the options will get cheaper as prices increase. In this case, you’ll make more money on a break in the underlying than you would a rally.

In my next installment, we’ll cover how changes in volatility will affect this trade, discuss more strategies, and if I’m feeling super ambitious, we’ll even do some real execution.