Pricing and hedging of financial derivatives: an approach via Backward Stochastic Differential Equations

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 ).