Trading Options in Turbulent Markets: Master Uncertainty through Active Volatility Management

Chapter 5. Extreme Volatility and Option Delta

The risks associated with options include, among other things, asset prices moving up or down, implied volatility moving up or down, and options losing value as time passes. These risks can be quantified with numbers generated by mathematical formulas known as greeks, because most use Greek letters as names. Each greek estimates the risk for one variable.

• Delta measures the change in the option price due to a change in the asset price.

• Gamma measures the change in the option delta due to a change in the asset price.

• Theta measures the change in the option price due to the passage of time.

• Vega measures the change in the option price due to a change in volatility.

• Rho measures the change in the option price due to a change in interest rates.

The Misnomer of Delta and Probability of Exercise

Over the years, a tricky issue regarding the delta of an option has emerged. It makes intuitive sense to illustrate delta initially using a simple equiprobable tree (i.e., 50 percent probability of either an up or down change in an asset) to price a call option and explain the concept of option sensitivity. However, this approach is flawed because of the conceptual problem of equating the delta of an option with the probability that the asset will finish in the money.

Delta ≠ The Probability of Exercise

Old-school traders, who learned the options business on the floor and not through a mathematical degree, experience a sharp learning curve to fully understand ...