The Elasticity and Risk Premium of an Option Portfolio: Practice Problems and Solutions
The Actuary's Free Study Guide for Exam 3F / Exam MFE - Section 44
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 44 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. See Section 42 here. See Section 43 here.
The elasticity of a portfolio of call options can be expressed as
Ωportfolio = i=1nΣωiΩ i where Ω i is the elasticity of the ith call option and ωi is the percentage of the portfolio comprised of the ith call option.
The risk premium on the portfolio - where all call options are based on the same underlying asset - is
γ - r = Ωportfolio(α - r)
Meaning of variables:
γ = expected annual continuously compounded return on the option.
α = expected annual continuously compounded return on the underlying asset (most often a stock).
Ω = option elasticity.
r = annual continuously compounded risk-free interest rate.
Source: McDonald, R.L., Derivatives Markets (Second Edition), Addison Wesley, 2006, Ch. 12,
p. 395 and this erratum.
Original Practice Problems and Solutions from the Actuary's Free Study Guide:
Remember that these formulas apply to portfolios of call options on the same underlying asset.
Comments
Important Clarification Note: In this section, ω_i denotes the percentage of the *value* of a portfolio comprised of the ith call option. It is not necessarily the same as ω_i in Section 41, which denotes the percentage of the portfolio (in terms of number of options) comprised of the ith call option. To all of the problems in this section, we add one assumption: THE PRICES OF ALL THE DIFFERENT OPTIONS ARE IDENTICAL.
Comment 1 (of 1)
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