Option Pricing and Hedging for Discrete Time Autoregressive Hidden Markov Model

TL;DR

This paper develops a discrete-time option pricing and hedging framework using a multivariate autoregressive hidden Markov model that captures time-varying volatility and serial dependence, validated through empirical tests on S&P 500 data.

Contribution

It introduces a novel autoregressive hidden Markov model for option pricing and hedging, outperforming traditional models in capturing financial time series properties.

Findings

Model fits S&P 500 returns better than standard HMMs.

Out-of-sample hedging performs well against Black-Scholes.

Theoretical prices improve hedging strategies.

Abstract

In this paper we solve the discrete time mean-variance hedging problem when asset returns follow a multivariate autoregressive hidden Markov model. Time dependent volatility and serial dependence are well established properties of financial time series and our model covers both. To illustrate the relevance of our proposed methodology, we first compare the proposed model with the well-known hidden Markov model via likelihood ratio tests and a novel goodness-of-fit test on the S\&P 500 daily returns. Secondly, we present out-of-sample hedging results on S\&P 500 vanilla options as well as a trading strategy based on theoretical prices, which we compare to simpler models including the classical Black-Scholes delta-hedging approach.