Abstract

We address risk minimizing option pricing in a semi-Markov modulated market where the floating interest rate depends on a finite state semi-Markov process. The growth rate and the volatility of the stock also depend on the semi-Markov process. Using the Föllmer–Schweizer decomposition we find the locally risk minimizing price for European options and the corresponding hedging strategy. We develop suitable numerical methods for computing option prices.

MSC codes

  1. 91B28
  2. 91B70

Keywords

  1. semi-Markov modulated market
  2. minimal martingale measure
  3. locally risk minimizing option price
  4. Black–Scholes equations

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Published In

cover image SIAM Journal on Control and Optimization
SIAM Journal on Control and Optimization
Pages: 1519 - 1541
ISSN (online): 1095-7138

History

Submitted: 27 February 2008
Accepted: 7 January 2009
Published online: 1 May 2009

MSC codes

  1. 91B28
  2. 91B70

Keywords

  1. semi-Markov modulated market
  2. minimal martingale measure
  3. locally risk minimizing option price
  4. Black–Scholes equations

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