Pricing and hedging of financial derivatives: an approach via Backward Stochastic Differential Equations
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Saudi Digital Library
Abstract
This paper studies backward stochastic differential equations driven by a Brownian motion and
their applications, concentrating on the financial applications. This study aims to determine a fair
price and a hedging strategy for European options with payoff 𝜂 using BSDEs. The underlying
market models are the extended Black-Scholes model and a market model with imperfections,
which has a different interest rate for borrowing and lending and a fixed tax. It was found that any
payoff 𝜂 can be replicated by a linear and unique self-financing portfolio (𝑉𝑡
) in the extended
Black-Scholes model whereas in the market model with imperfections, any payoff 𝜂 can be
replicated by a nonlinear and unique self-financing portfolio (𝑉𝑡
).