Option Pricing and Hedging for Discrete Time Autoregressive Hidden Markov Model
This work addresses hedging and pricing challenges for financial practitioners by extending models to better fit real-world time series, though it appears incremental as it builds on existing hidden Markov models.
The authors tackled the problem of mean-variance hedging for asset returns modeled with a multivariate autoregressive hidden Markov model, capturing time-dependent volatility and serial dependence, and demonstrated its relevance through out-of-sample hedging on S&P 500 options, showing comparisons to simpler models like Black-Scholes delta-hedging.
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.