Convergence of numerical methods for valuing path-dependent options using interpolation

One method for valuing path-dependent options is the augmented state space approach described in Hull and White (1993) and Barraquand and Pudet (1996), among others. In certain cases, interpolation is required because the number of possible values of the additional state variable grows exponentially. We provide a detailed analysis of the convergence of these algorithms. We show that it is possible for the algorithm to be non-convergent, or to converge to an incorrect answer, if the interpolation scheme is selected in appropriately. We concentrate on Asian options, due to their popularity and because of some errors in the previous literature. Copyright Kluwer Academic Publishers 2002Convergance, forward shooting grid, interpolation, option pricing, path-dependence,

Convergence Of Numerical Methods For Valuing Path-Dependent Options Using Interpolation

One method for valuing path-dependent options is the augmented state space approach described in Hull and White (1993) and Barraquand and Pudet (1996), among others. In certain cases, interpolation is required because the number of possible values of the additional state variable grows exponentially. We provide a detailed analysis of the convergence of these algorithms. We show that it is possible for the algorithm to be non-convergent, or to converge to an incorrect answer, if the interpolation scheme is selected inappropriately. We concentrate on Asian options, due to their popularity and because of some errors in the previous literature

An Object-Oriented Framework For Valuing Shout Options on High-Performance Computer Architectures

A shout option is a financial contract which allows the holder to change the payoff during the lifetime of the contract. For example, the holder could have the right to set the strike price to the current value of the underlying asset. Complex versions of these options are embedded in financial products which offer various types of maturity guarantees such as segregated funds marketed by Canadian insurance companies. The value of these options can be determined by solving a collection of coupled partial differential equations (PDEs). In this work we develop an extensible, object-oriented framework for valuing these contracts which is capable of exploiting modern, high-performance supercomputing architectures. We use this framework to study and illustrate practical aspects of valuing and hedging these contracts