Option Greeks: Theta, Rho, Psi, and Greek Measures for Portfolios: Practice Problems and Solutions

The Actuary's Free Study Guide for Exam 3F / Exam MFE - Section 41

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 41 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. See Section 40 here.

Theta

The option Greek theta (θ) "measures the change in the option price when there is a decrease in the time to maturity of 1 day" (McDonald 2006, p. 383).

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

In most cases, theta is negative - that is, an option loses value as expiration time approaches. The fastest time decay at expiration occurs for at-the-money options.

There are a few exceptions to this rule. Theta can be positive for deep in-the-money European puts and deep in-the-money European calls when the underlying asset has a high dividend yield.

Rho

The option Greek rho (ρ) "measures the change in the option price when there is an increase in the interest rate of 1 percentage point (100 basis points)" (McDonald 2006, p. 383).

R. L. McDonald suggests the following mnemonic device to help memorize the definition of rho: "rho" begins with the letter r, which is commonly used to denote the annual continuously-compounded risk-free interest rate.

For an ordinary call option, rho is positive; for a put, rho is negative.

Psi