On Pricing Barrier Options with Discrete Monitoring
نویسندگان
چکیده
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 applied to pricing path-dependent derivatives with discrete monitoring, the paper presents an analytic (approximation) formula for valuation of discrete barrier options under stochastic volatility environment. To our knowledge, this paper is the first one that shows an analytical approximation for pricing discrete barrier options with stochastic volatility models. Finally, it provides numerical examples for pricing double barrier call options with discrete monitoring under the Heston model.
منابع مشابه
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 کاملA Continuity Correction for Discrete Barrier Options
The payoff of a barrier option depends on whether or not a specified asset price, index, or rate reaches a specified level during the life of the option. Most models for pricing barrier options assume continuous monitoring of the barrier; under this assumption, the option can often be priced in closed form. Many (if not most) real contracts with barrier provisions specify discrete monitoring in...
متن کاملBarrier 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 کاملNumerical pricing of discrete barrier and lookback options via Laplace transforms
URL: www.thejournalofcomputationalfinance.com Most contracts of barrier and lookback options specify discrete monitoring policies. However, unlike their continuous counterparts, discrete barrier and lookback options essentially have no analytical solution. For a broad class of models, including the classical Brownian model and jump-diffusion models, we show that the Laplace transforms of discre...
متن کاملOn Pricing of Discrete Barrier Options
A barrier option is a derivative contract that is activated or extinguished when the price of the underlying asset crosses a certain level. Most models assume continuous monitoring of the barrier. However, in practice, most, if not all, of the barrier options traded are discretely monitored. Unlike their continuous counterparts, there is essentially no closed form solution available, and even n...
متن کامل