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Goswami, Anindya
Saini, Ravi Kant
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[Journal:] Cogent Economics & Finance [ISSN:] 2332-2039 [Volume:] 2 [Year:] 2014 [Issue:] 1 [Pages:] 1-11
It is known that the risk minimizing price of European options in Markovmodulated market satisfies a system of coupled PDE, known as generalized B-S-M PDE. In this paper, another system of equations, which can be categorized as a Volterra integral equations of second kind, are considered. It is shown that this system of integral equations has smooth solution and the solution solves the generalized B-S-M PDE. Apart from showing existence and uniqueness of the PDE, this IE representation helps to develop a new computational method. It enables to compute the European option price and corresponding optimal hedging strategy by using quadrature method.
Markov modulated market
locally risk minimizing option price
Black-Scholes-Merton equations
Volterra equation
quadrature method
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