Understanding Option Pricing


As you could probably guess, option pricing determines the prices of options. Simple, right? Not so fast…

Option pricing is where the greeks come into play. When you buy a stock, you participate in both upside and downside moves of the stock on a 1-to-1 basis. Options, and out-of-the-money options in particular, allow you to participate in both upside and downside moves on a lot more than a 1-to-1 basis. Options are a bit like stepping from flatland to a world of higher dimensions.

The Greeks in Option Pricing

Delta is the first greek to know in option pricing. It measures the change in the option price for changes in the underlying stock price. An option is said to be at-the-money when the stock is trading near the strike price. At-the-money options tend to trade with a delta of 0.5 meaning that for each $1 move in the stock, the option will move $0.50 all else being equal.

Delta ranges from 0 to 1. Delta is also known as the hedge ratio or the amount of shares you would need to neutralize the dollar value of price moves. Delta can also be thought of as the market’s estimate of the probability that the option will expire in the money. In other words, if an option has a delta of 0.5, the market is assigning a 50% probability to the option finishing in the money. If your research tells you the real probability is 70%, then you can buy the option and have a positive expected value based on your research.

As expiration approaches, delta on in-the-money options will approach 1 and delta on out-of-the-money options will approach 0. So deltas change with time.

Gamma is the second greek to know for option pricing. Gamma measures the rate of change in delta for changes in the underlying stock price. As moneyness increases, the stock’s delta increases and that change in delta is gamma.

The Time Component

The third greek is theta which measures the option’s sensitivity to time. All else being equal, options lose value over time with the fastest declines as expiration approaches. Investors often refer to the effects of theta as time decay.

The fourth greek is vega and measures the option’s sensitivity to volatility. With stocks, you always have a delta of 1. With options, you have a view on time and expected volatility as well. You can be right on direction, but if you overpay for vega you can still lose money.

The final greek is rho which measures the sensitivity of an option to interest rates. As rates rise, call option values tend to increase.

An overview of option pricing greeks:

delta = change in options price for change in underlying asset

gamma = rate of change in delta

theta = options sensitivity to time (time decay)

vega = options sensitivity to volatility

rho = options sensitivity to interest rates

In options trading, you frequently need a view on both direction and volatility. At the end of the day, merely understanding the elements of option pricing will put you ahead of other market participants.

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