Pricing Double-Barrier Options Using the Boundary Element Method
نویسندگان
چکیده
A numerical method to price double-barrier options with moving barriers is proposed. Using the so-called Boundary Element Method, an integral representation of the double-barrier option price is derived in which two of the integrand functions are not given explicitly but must be obtained solving a system of Volterra integral equations of the first kind. This system of equations is affected by several kinds of singularities, therefore it is first regularized and then solved using a low-order finite element method based on product integration. Several numerical experiments are carried out showing that the method proposed is extraordinarily fast and accurate, also when the barriers are not differentiable functions. Moreover the numerical algorithm presented in this paper performs significantly better than the finite difference approach. JEL Classification Codes: C02, C63, G13
منابع مشابه
Barrier options pricing of fractional version of the Black-Scholes model
In this paper two different methods are presented to approximate the solution of the fractional Black-Scholes equation for valuation of barrier option. Also, the two schemes need less computational work in comparison with the traditional methods. In this work, we propose a new generalization of the two-dimensional differential transform method and decomposition method that will extend the appli...
متن کاملOn Pricing of the Up-and-Out Call–A Boundary Integral Method Approach
The payoffs of the barrier options depend on the time path of the underlying price as opposed to just the price at expiry. It implies that both the boundary conditions and the initial condition are imposed on the Black-Scholes partial differential equation. Therefore, the valuation of the barrier options is a boundary value problem. Since the Black-Scholes equation can be converted into a homog...
متن کاملValuation of Continuously Monitored Double Barrier Options and Related Securities
In this paper, we apply Carr’s randomization approximation and the operator form of theWiener-Hopf method to double barrier options in continuous time. Each step in the resulting backward induction algorithm is solved using a simple iterative procedure that reduces the problem of pricing options with two barriers to pricing a sequence of certain perpetual contingent claims with first-touch sing...
متن کاملOption pricing under the double stochastic volatility with double jump model
In this paper, we deal with the pricing of power options when the dynamics of the risky underling asset follows the double stochastic volatility with double jump model. We prove efficiency of our considered model by fast Fourier transform method, Monte Carlo simulation and numerical results using power call options i.e. Monte Carlo simulation and numerical results show that the fast Fourier tra...
متن کاملPricing European Barrier Options with Partial Differential Equations
Barrier options were first priced by Merton in 1973 using partial differential equation. In this work, we present a closed form formula for pricing European barrier option with a moving barrier that increases with time to expiration. We adopted a three-step approach which include; justifying that barrier options satisfy the Black-Scholes partial differential equation under certain conditions, p...
متن کامل