2011•Journal of applied mathematics & informaticsRequires access

BARRIER OPTION PRICING UNDER THE VASICEK MODEL OF THE SHORT RATE

Yudong Sun, Yimin Shi, Xin Gu

Abstract

In this study, assume that the stock price obeys the stochastic differential equation driven by mixed fractional Brownian motion, and the short rate follows the Vasicek model. Then, the Black-Scholes partial differential equation is held by using fractional Ito formula. Finally, the pricing formulae of the barrier option are obtained by partial differential equation theory. The results of Black-Scholes model are generalized.

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Available abstract

Key concepts: Vasicek model, Mathematics, Partial differential equation, Stochastic differential equation, Black–Scholes model, Barrier option, Short rate, Valuation of options