Pricing Options in Markov-Modulated Fractional Brownian Markets
The Markov-modulated (B; S)-securities market is a (B; S)-security market, consisting of riskless asset, bond B; and risky asset, stock S; in random media X; or (B; S)-security market driven by a Markov process xt 2 X: We study the pricing options for Markovmodulated fractional Brownian (B; S)-security markets, including Hu & ksendal (1999) and Elliott & van der Hoek (2000) schemes. Incompleteness of Markov-modulated fractional Brownian (B; S)-security markets in Hu & ksendal and Elliott & van der Hoek schemes without and with jumps are established and Black-Scholes formulae for these schemes are derived. Perfect hedging in a Markov-modulated Brownian fractional (B; S)-security market (without and with jumps) is not possible since we have an incomplete market. Following the idea proposed by Follmer and Sondermann (1986) and Follmer and Schweizer (1993) we look for the strategy locally minimizing the risk. The residual risk processes are presented in these two schemes.
Year of publication: |
2007-11-26
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Authors: | Elliott, Robert ; Swishchuk, Anatoliy |
Institutions: | Department of Economics, University of Calgary |
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