On pricing discrete barrier options using conditional expectation and importance sampling Monte Carlo
نویسندگان
چکیده
Estimators for the price of a discrete barrier option based on conditional expectation and importance sampling variance reduction techniques are given. There are erroneous formulas for the conditional expectation estimator published in the literature: we derive the correct expression for the estimator. We use a simulated annealing algorithm to estimate the optimal parameters of exponential twisting in importance sampling, and compare it with a heuristic used in the literature. Randomized quasi-Monte Carlo methods are used to further increase the accuracy of the estimators. c © 2007 Elsevier Ltd. All rights reserved.
منابع مشابه
Conditional sampling for barrier option pricing under the Heston model
We propose a quasi-Monte Carlo algorithm for pricing knock-out and knock-in barrier options under the Heston (1993) stochastic volatility model. This is done by modifying the LT method from Imai and Tan (2006) for the Heston model such that the first uniform variable does not influence the stochastic volatility path and then conditionally modifying its marginals to fulfill the barrier condition...
متن کاملNumerical Methods for Discrete DoubleBarrier Option Pricing Based on Merton Jump Diffusion Model
As a kind of weak-path dependent options, barrier options are an important kind of exotic options. Because the pricing formula for pricing barrier options with discrete observations cannot avoid computing a high dimensional integral, numerical calculation is time-consuming. In the current studies, some scholars just obtained theoretical derivation, or gave some simulation calculations. Others i...
متن کاملVariance Reduction Techniques of Importance Sampling Monte Carlo Methods for Pricing Options
In this paper we discuss the importance sampling Monte Carlo methods for pricing options. The classical importance sampling method is used to eliminate the variance caused by the linear part of the logarithmic function of payoff. The variance caused by the quadratic part is reduced by stratified sampling. We eliminate both kinds of variances just by importance sampling. The corresponding space ...
متن کاملApplication of Monte Carlo Simulation in the Assessment of European Call Options
In this paper, the pricing of a European call option on the underlying asset is performed by using a Monte Carlo method, one of the powerful simulation methods, where the price development of the asset is simulated and value of the claim is computed in terms of an expected value. The proposed approach, applied in Monte Carlo simulation, is based on the Black-Scholes equation which generally def...
متن کاملA Martingale Control Variate Method for Option Pricing with Stochastic Volatility
A generic control variate method is proposed to price options under stochastic volatility models by Monte Carlo simulations. This method provides a constructive way to select control variates which are martingales in order to reduce the variance of unbiased option price estimators. We apply a singular and regular perturbation analysis to characterize the variance reduced by martingale control v...
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:
- Mathematical and Computer Modelling
دوره 47 شماره
صفحات -
تاریخ انتشار 2008