alexa Pricing Options and Variance Swaps in Markov-Modulated Brownian Markets
Mathematics

Mathematics

Journal of Applied & Computational Mathematics

Author(s): Robert J Elliott, Anatoliy V Swishchuk

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A Markov-modulated market consists of a riskless asset or bond, B, and a risky asset or stock, S, whose dynamics depend on Markov process x. We study the pricing of options and variance swaps in such markets. Using the martingale characterization of Markov processes, we note the incompleteness of Markov-modulated markets and find the minimal martingale measure. Black-Scholes formulae for Markov-modulated markets with or without jumps are derived. Perfect hedging in a Markov-modulated Brownian and a fractional Brownian market is not possible as the market is incomplete. Following the idea proposed by Föllmer and Sondermann and Föllmer and Schweizer we look for the strategy which locally minimizes the risk. The residual risk processes are determined in these situations. Variance swaps for stochastic volatility driven by Markov process are also studied

This article was published in International Series in Operations Research & Management Science and referenced in Journal of Applied & Computational Mathematics

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