Option Pricing and Hedging for Discrete Time Autoregressive Hidden Markov Model

Massimo Caccia and Bruno Rémillard

Chapter 12 in Innovations in Insurance, Risk- and Asset Management:Proceedings of the Innovations in Insurance, Risk- and Asset Management Conference, 2018, pp 313-348 from World Scientific Publishing Co. Pte. Ltd.

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 recommended approach, 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. In addition, we present out-of-sample hedging results on S&P 500 vanilla options as well as a trading strategy based on the difference between theoretical and market prices. This strategy is compared to simpler models including the classical Black-Scholes delta-hedging approach.

Keywords: Insurance; Actuarial Science; Risk Measure; Reinsurance; Copula; Replicating Portfolio; Bayesian Finance; Risk Classification; Stochastic Dominance; Dynamic Hedging; Autoregressive Hidden Markov Models; Exchange-Traded Funds; Uncertainty Quantification; Fixed Income; Stochastic Processes for Finance (search for similar items in EconPapers)
JEL-codes: G22 G32 (search for similar items in EconPapers)
Date: 2018
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