An Algorithm for the Pricing of Path-Dependent American Options using Malliavin Calculus
نویسنده
چکیده
We propose a recursive scheme to calculate backward the values of conditional expectations of functions of path values of Brownian motion. This schemes is based on the Clark-Ocone formula in discrete time. We construct an algorithm based our scheme to effectively calculate the price of American options on securities with path-dependent payoffs. Our algorithm remedies the decrease of performance experienced by regression-based Monte Carlo when the dimensionality of the necessary regressands becomes large due to path-dependence.
منابع مشابه
On Pricing Barrier Options with Discrete Monitoring
This paper proposes a new approximation method for pricing barrier options with discrete monitoring under stochastic volatility environment. In particular, the integration-by-parts formula and the duality formula in Malliavin calculus are effectively applied in an asymptotic expansion approach. First, the paper derives an asymptotic expansion for generalized Wiener functionals. After it is appl...
متن کاملMonte Carlo methods for pricing and hedging American options in high dimension
We numerically compare some recent Monte Carlo algorithms devoted to the pricing and hedging American options in high dimension. In particular, the comparison concerns the quantization method of Barraquand-Martineau and an algorithm based on Malliavin calculus. The (pure) Malliavin calculus algorithm improves the precision of the computation of the delta but, merely for pricing purposes, is unc...
متن کاملA Differential Tree Approach to Price Path-Dependent American Options using Malliavin Calculus
We propose a recursive schemes to calculate backward the values of conditional expectations of functions of path values of Brownian motion. This scheme is based on the Clark-Ocone formula in discrete time. We suggest an algorithm based on our scheme to effectively calculate the price of American options on securities with path-dependent payoffs. For problems where the pathdependence comes only ...
متن کاملComputation of Greeks using Binomial Tree
This paper proposes a new efficient algorithm for the computation of Greeks for options using the binomial tree. We also show that Greeks for European options introduced in this article are asymptotically equivalent to the discrete version of Malliavin Greeks. This fact enables us to show that our Greeks converge to Malliavin Greeks in the continuous time model. The computation algorithms of Gr...
متن کاملPricing and Hedging Asian Basket Options with Quasi-Monte Carlo Simulations
In this article we consider the problem of pricing and hedging high-dimensional Asian basket options by Quasi-Monte Carlo simulation. We assume a Black-Scholes market with time-dependent volatilities and show how to compute the deltas by the aid of the Malliavin Calculus, extending the procedure employed by Montero and Kohatsu-Higa [1]. Efficient path-generation algorithms, such as Linear Trans...
متن کاملذخیره 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 2008