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Option Pricing and Hedging for Discrete Time Autoregressive Hidden Markov Model

In: Innovations in Insurance, Risk- and Asset Management

Author

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  • Massimo Caccia
  • Bruno Rémillard

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.

Suggested Citation

  • Massimo Caccia & Bruno Rémillard, 2018. "Option Pricing and Hedging for Discrete Time Autoregressive Hidden Markov Model," World Scientific Book Chapters, in: Kathrin Glau & Daniël Linders & Aleksey Min & Matthias Scherer & Lorenz Schneider & Rudi Zagst (ed.), Innovations in Insurance, Risk- and Asset Management, chapter 12, pages 313-348, World Scientific Publishing Co. Pte. Ltd..
    • Handle: RePEc:wsi:wschap:9789813272569_0012
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    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;
    All these keywords.

    JEL classification:

    • G22 - Financial Economics - - Financial Institutions and Services - - - Insurance; Insurance Companies; Actuarial Studies
    • G32 - Financial Economics - - Corporate Finance and Governance - - - Financing Policy; Financial Risk and Risk Management; Capital and Ownership Structure; Value of Firms; Goodwill

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