Option Greeks: Gamma and Vega: Practice Problems and Solutions

The Actuary's Free Study Guide for Exam 3F / Exam MFE - Section 40

This section of sample problems and solutions is a part of The Actuary's Free Study Guide for Exam 3F / Exam MFE, authored by Mr. Stolyarov.

This is Section 40 of the Study Guide. See Section 1 here. See Section 2 here. See Section 3 here. See Section 4 here. See Section 5 here. See Section 6 here. See Section 7 here. See Section 8 here. See Section 9 here. See Section 10

here. See Section 11 here. See Section 12 here. See Section 13 here. See Section 14 here. See Section 15 here. See Section 16 here. See Section 17 here. See Section 18 here. See Section 19 here. See Section 20 here. See Section 21 here. See Section 22 here. See Section 23 here. See Section 24 here. See Section 25 here. See Section 26 here. See Section 27 here. See Section 28 here. See Section 29 here. See Section 30 here. See Section 31 here. See Section 32 here. See Section 33 here. See Section 34 here. See Section 35 here. See Section 36 here. See Section 37 here. See Section 38 here. See Section 39 here.

The option Greek gamma (Γ) "measures the change in delta when the stock price increases by $1" (McDonald 2006, p. 382).

Whether a call or a put is purchased, gamma is positive. Thus, delta increases as the stock price increases.

"For a call, delta approaches 1 as the stock price increases. For a put, delta approaches 0 as the stock price increases" (McDonald 2006, p. 384).

For a call and a put with the same strike price and time to expiration, gamma is the same.

Deep in-the-money and out-of-the money options both have values of gamma close to 0.

The option Greek vega "measures the change in the option price when there is an increase in volatility of one percentage point" (where one percentage point = 0.01).

R. L. McDonald suggests the following mnemonic device to help memorize the definition of vega: "vega" and "volatility" begin with the same letter.

The higher the volatility of the underlying asset price, the higher the price of both the call and put options on that asset. Thus, vega is positive for purchased calls and puts.