A continuous dependence result for ultra - parabolic equations in option pricing

نویسندگان

  • Marco Di Francesco
  • Andrea Pascucci
چکیده

We prove continuous dependence results for solution to the Cauchy problem related to degenerate parabolic equations arising in the valuation of financial derivatives. These results are crucial in some standard calibration procedure for recent stochastic volatility and interest rates models.

برای دانلود رایگان متن کامل این مقاله و بیش از 32 میلیون مقاله دیگر ابتدا ثبت نام کنید

ثبت نام

اگر عضو سایت هستید لطفا وارد حساب کاربری خود شوید

منابع مشابه

Valuation of installment option by penalty method

In this paper, installment options on the underlying asset which evolves according to Black-Scholes model and pays constant dividend to its owner will be considered. Applying arbitrage pricing theory, the non-homogeneous parabolic partial differential equation governing the value of installment option is derived. Then, penalty method is used to value the European continuous installment call opt...

متن کامل

Local vs Non-local Forward Equations for Option Pricing

When the underlying asset is a continuous martingale, call option prices solve the Dupire equation, a forward parabolic PDE in the maturity and strike variables. By contrast, when the underlying asset is described by a discontinuous semimartingale, call prices solve a partial integro-differential equation (PIDE), containing a non-local integral term. We show that the two classes of equations sh...

متن کامل

Numerical Solutions for Fractional Black-Scholes Option Pricing Equation

In this article we have applied a numerical finite difference method to solve the Black-Scholes European and American option pricing both presented by fractional differential equations in time and asset.

متن کامل

Optimal continuous dependence estimates for fractional degenerate parabolic equations

We derive continuous dependence estimates for weak entropy solutions of degenerate parabolic equations with nonlinear fractional diffusion. The diffusion term involves the fractional Laplace operator, ∆α/2 for α ∈ (0, 2). Our results are quantitative and we exhibit an example for which they are optimal. We cover the dependence on the nonlinearities, and for the first time, the Lipschitz depende...

متن کامل

Numerical algorithm for discrete barrier option pricing in a Black-Scholes model with stationary process

In this article, we propose a numerical algorithm for computing price of discrete single and double barrier option under the emph{Black-Scholes} model. In virtue of some general transformations, the partial differential equations of option pricing in different monitoring dates are converted into simple diffusion equations. The present method is fast compared to alterna...

متن کامل

ذخیره در منابع من


  با ذخیره ی این منبع در منابع من، دسترسی به آن را برای استفاده های بعدی آسان تر کنید

عنوان ژورنال:

دوره   شماره 

صفحات  -

تاریخ انتشار 2007