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Zbl 1188.91222
Siu, Tak Kuen; Yang, Hailiang
Option pricing when the regime-switching risk is priced. (English)
[J] Acta Math. Appl. Sin., Engl. Ser. 25, No. 3, 369-388 (2009). ISSN 0168-9673; ISSN 1618-3932/e

{\it J. D. Hamilton} [Econometrica 57, No.~2, 357--384 (1989; Zbl 0685.62092)] introduced a class of discrete-time Markov-switching autoregressive time-series models in which the random regime-switching is governed by another underlying process, namely a discrete-time finite-state Markov chain. The main challenge of the option valuation problem under regime-switching models consists in determining an equivalent martingale measure so that the regime-switching risk and the diffusion risk are approximately priced. The authors of the present paper (motivated by Hamilton's paper (loc. cit.)) consider the pricing of an option when the price dynamics of the underlying risky asset is governed by a Markov-modulated geometric Brownian motion. It is assumed, that the drift and the volatility of the underlying risky asset are depending on an observable continuous-time, finite-state Markov chain whose states represent observable states of an economy. Based on the Esscher transform, a set of equivalent martingale measures is determined.\par At a second step, an equivalent martingale pricing measure is specified by minimizing the maximum entropy between an equivalent martingale measure and the real-world probability measure over different economic states. In addition, the authors present numerical procedures for the computation of option prices. The results indicate that there is a significant impact of pricing regime-switching risk on option prices.
[Klaus Schürger (Bonn)]

MSC 2000:: *91G20
60G44 Martingales with continuous parameter

Keywords: option valuation; regime-switching risk; two-stage pricing procedure; Esscher transform; martingale restriction; min-max entropy problem

Citations: Zbl 0685.62092

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