The Elasticity and Risk Premium of an Option Portfolio

The elasticity of a portfolio of call options can be expressed as

Ω_portfolio = _i=1ⁿΣω_iΩ _i where Ω _i is the elasticity of the ith call option and ω_i 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 = Ω_portfolio(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