Option Elasticity and Option Volatility: Practice Problems and Solutions

The Actuary's Free Study Guide for Exam 3F / Exam MFE - Section 42

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 42 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. See Section 41 here.

The formula for option elasticity Ω is

Ω = [% change in option price]/[% change in stock price] = S∆/C, where C is the option price, S is the stock price, and ∆ is the option delta.

For a call option, Ω ≥ 1. Ω decreases as the strike price K increases.

For a put option, Ω ≤ 0.

The volatility of an option can be expressed as

σ_option = σ_stock*│Ω│. That is, option price volatility is stock price volatility multiplied by the absolute value of option elasticity.

Source: McDonald, R.L., Derivatives Markets (Second Edition), Addison Wesley, 2006, Ch. 12, pp. 391-394.

Original Practice Problems and Solutions from the Actuary's Free Study Guide:

Problem OEOV1. The stock of Assiduous Co. trades for $123 per share with a price volatility of 0.3. Certain call options on Assiduous Co. stock have a delta of 0.44 and a price of $20. Find the elasticity of such a call option.

Solution OEOV1. We use the formula Ω = S∆/C = 123*0.44/20 = Ω = 2.706