Ӧ�ø���ͳ�� 2013, 29(2) 179-187 DOI:      ISSN: 1001-4268 CN: 31-1256

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The MEMMs for Markov-Modulated GBMs
Wang Bo, Song Ruili
School of Applied Mathematics, Nanjing University of Finance and Economics
Abstract:

In this paper, we consider the option
pricing problem when the risky underlying assets are driven by
Markov-modulated geometric Brownian motion (GBM). That is, the
market parameters, for instance, the market interest rate, the
appreciation rate and the volatility of the risky asset, depend on
unobservable states of the economy which are modeled by a
continuous-time hidden Markov chain. The market described by the
Markov-modulated GBM model is incomplete in general, and, hence, the
martingale measure is not unique. We adopt the minimal relative
entropy martingale measure (MEMM) for the Markov-modulated GBM model
as the suitable martingale measure and we obtain the MEMM for the
market in general sense.

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