TITLE:
Random Timestepping Algorithm with Exponential Distribution for Pricing Various Structures of One-Sided Barrier Options
AUTHORS:
Hasan Alzubaidi
KEYWORDS:
Barrier Option with Rebate Payment, Binary Barrier Option, Partial Barrier Option, Hitting Time Error, Exponential Time-Stepping Algorithm
JOURNAL NAME:
American Journal of Computational Mathematics,
Vol.7 No.3,
August
3,
2017
ABSTRACT: The
exponentially-distributed random timestepping algorithm with boundary test is
implemented to evaluate the prices of some variety of single one-sided barrier
option contracts within the framework of Black-Scholes model, giving efficient
estimation of their hitting times. It is numerically shown that this algorithm,
as for the Brownian bridge technique, can improve the rate of weak convergence
from order one-half for the standard Monte Carlo to order 1. The exponential timestepping
algorithm, however, displays better results, for a given amount of CPU time,
than the Brownian bridge technique as the step size becomes larger or the
volatility grows up. This is due to the features of the exponential distribution
which is more strongly peaked near the origin and has a higher kurtosis
compared to the normal distribution, giving more stability of the exponential timestepping
algorithm at large time steps and high levels of volatility.