Role of Gamma Risk in Options Trading

Gamma measures the risk that remains once the portfolio is delta neutral (non-linearity risk).

The BSM model assumes that share prices change continuously with time. In reality, stock prices do not move continuously. Instead, they often jump, and this creates gamma risk. 

Gamma risk is so-called because gamma measures the risk of share prices jumping when hedging an options position, leaving an otherwise hedged option position abruptly unhedged.

A delta-hedged portfolio is said to have a negative net gamma exposure if it has short position in calls and a long position in stocks.

Question

Which of the following statements is most accurate:

1. Gamma measures linearity risk
2. Gamma risk is created when stock prices move continuously
3. Gamma risk results from share prices jumping when hedging an options position, leaving the hedged position suddenly unhedged

Solution

The correct answer is C:

Gamma risk is so-called because gamma measures the risk of share prices jumping when hedging an options position, leaving an otherwise hedged option position abruptly unhedged.

A is incorrect: Gamma measures non-linearity risk, i.e., the risk that remains once the portfolio is delta neutral.

B is incorrect: The BSM model assumes that share prices change continuously with time. In reality, stock prices do not move continuously. Instead, they often jump, and this creates gamma risk.

Reading 38: Valuation of Contingent Claims

LOS 38 (m) Describe the role of gamma risk in options trading;