Option Pricing in an Investment Risk-Return Setting

TL;DR

This paper integrates modern portfolio theory with option pricing to develop optimal hedging strategies across various underlying asset models, enhancing risk management at maturity.

Contribution

It introduces a unified framework for constructing optimal portfolios that hedge European options under multiple complex asset price dynamics.

Findings

Derived optimal holdings for mean-variance portfolios.

Quantified unhedged risk prior to maturity.

Provided solutions for diverse asset price models.

Abstract

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 follow discrete binomial price dynamics, continuous diffusions, stochastic volatility, volatility-of-volatility, and Merton-jump diffusion are derived.