Option Pricing in an Investment Risk-Return Setting
25 Pages Posted: 1 Aug 2019
Date Written: July 29, 2019
In this paper, we combine modern portfolio theory and option pricing theory so that a trader who takes a position in a European option contract and the underlying assets can construct an optimal portfolio such that at the moment of the contract’s maturity the contract is perfectly hedged. We derive both the optimal holdings in the underlying assets for the trader’s optimal mean-variance portfolio and the amount of unhedged risk prior to maturity. Solutions assuming the cases where the price dynamics in the underlying assets follows discrete binomial price dynamics, continuous diffusions, stochastic volatility, volatility-of-volatility, and Merton-jump diffusion are derived.
Keywords: option pricing; mean-variance portfolio; binomial pricing trees; stochastic continuous diffusions
JEL Classification: G13, G12, G19
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