My Millionaire Goal

The gamma of an option indicates how the delta of an option will change relative to a 1 point increase in the underlying asset. It is actually the “Delta of the Delta”…

For those Physics experts out there, we can say that
“Delta is to Velocity, as Gamma is to Acceleration”…

For Math experts, Delta is actually is the First Derivative of the Option Price (w.r.t. to Stock Price), while Gamma is the Second Derivative.

For everyone else… let me try to explain gamma with a hypothetical example

Suppose AAPL is currently trading at $190. Let’s look at how the price of a $205 CALL option will likely change when AAPL’s stock price changes

Understanding Gamma

From the table above, you’ll notice that the delta of an option changes at a different rate depending on how far the current stock price is from the option’s strike price. The further it is, the less the delta will change.

For instance, when the current stock price changes from $190 to $195 (a $5 change), the delta increased by 0.3. In contrast, when it changes from $200 to $205 (a $5 change as well), the delta increased by 0.15. This is because the delta of an option changes at the greatest rate when the option is at-the-money (highlighted in yellow).

Since the delta of an option changes at a different rate, the gamma is a measure specifically designed to measure this rate of change of delta.

As a tool, gamma can tell you how “stable” your delta is. A big gamma means that your delta can start changing dramatically for even a small move in the stock price. Personally, I don’t really worry too much about gamma when I trade… This may not be the best way to trade… but it has worked well for me and I really love to keep things simple… So… gamma? What gamma….????

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The last option greek to discuss is Rho…

Rho is an estimate of how much the theoretical value of an option changes when interest rates move 1.00%. For example, suppose a call option of stock ABC has a value of 2.1 with a Rho value of .19. If interest rates increase from 5% to 6%, then the price of the call option, theoretically at least will increase from 2.10 to 2.29.

Among all the Greeks, Rho is the least used… and it has the least effect on options price… so, naturally, I never looked at Rho when I trade…

To explain what vega is, we got to first look at a key concept in options pricing: Volatility.

Volatility is a measure of risk / uncertainty in the underlying stock price of an option. It reflects how likely the underlying stock price will fluctuate up or down. Some stocks tend to move wildly from one trading day to another, and thus have high volatility (and risk). Other stocks barely move for an entire week and have low volatility.

In options, there are 2 types of volatility:

1) Historical Volatility (HV), or sometimes called Statistical Volatility, is a measure of the fluctuations of the stock price over the past 30 trading days. If there is a sharp move in the stock price (up or down) during that period, the historical volatility will increase drastically. HV is obtained by calculating the standard deviation of historical daily prices over the period.

2) Implied Volatility (IV) is an estimate of the volatility of the stock price for the next 30 trading days.

This estimate is obtained by comparing the actual market price of an option with the theorectical price of the option calculated based on an options pricing model (e.g. The Black–Scholes Model). It is the volatility that, when used in a particular pricing model, yields a theoretical value for the option equal to the current market price of that option.

For instance, let’s consider a HYPOTHETICAL options pricing model.. Suppose

Theoretical Options Price = 0.09823*IV + 10.2

If the current market price of the option is $12, then to calculate what IV value will cause the theoretical price of the option to be equals to the actual market price, we have

12 = 0.09823*IV + 10.2

Thus IV = (12 – 10.2)/0.09823 = 18.32

In other words, IV is the volatility “implied” by the current market price of the options.

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Now, let’s get back to our options greek: VEGA…

Vega measures the sensitivity of an option’s price to changes in Implied Volatility (IV). It estimates how much an option price would change when implied volatility changes by 1%.

For instance, let’s assume the current price of AAPL Oct 190 Call is $3, with Vega 0.20 and the volatility of AAPL stock is 35%. If the volatility of AAPL increases to 36%, the AAPL Oct 190 Call’s price will rise to $3.20. If the volatility drops to 34%, the Call’s value will drop to $2.80.

An increase in IV will increase an options’s price for both Calls and Puts options. This makes sense, since the higher the volatility, the greater the probability that an option will move into your favor by expiration.

As an options seller, I love to sell when volatility is high, since I can sell the options at a higher price. However, honestly, although some traders trade purely based on options volatility, I’m not too concerned about it. What I normally do is simply check that the IV of the options I’m buying is lower (or at least not much higher) than that of the options I’m selling. Other than that, I do not really worry too much about volatility… As long as I can sell the iron condor (or other combinations) at my target price, I’m fine… If you are interested in finding out more about options volatility, you can check out this book  by Sheldon Natenber: Option Volatility & Pricing: Advanced Trading Strategies and Techniques

Just for Laughs: The Unfortunate Consequence of a Sudden Rise in Volatility of Belt Prices