Efficient Monte Carlo Algorithm Using Antithetic Variate and Brownian Bridge Techniques for Pricing the Barrier Options with Rebate Payments

Alzubaidi, Hamzah

doi:10.3844/jmssp.2016.1.11

Cited by 4 publications

(1 citation statement)

References 18 publications

(42 reference statements)

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“…A rebate is positive discount paid to the option holder incase of an a knock-out or knock-in and its presence increases the value of the barrier option, even though it has no effect on its payoff. Furthermore, Alzubaidi (2016) employed the concept of antithetic variate, together with the Brownian bridge to improve the efficiency of the Monte-Carlo methods in the valuation of rebate barrier options.…”

Section: Introductionmentioning

confidence: 99%

A Comparative Study on Barrier Option Pricing using Antithetic and Quasi Monte-Carlo Simulations

Umeorah¹,

Mashele²

2018

Journal of Mathematics and Statistics

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Monte-Carlo simulations have been utilized greatly in the pricing of derivative securities. Over the years, several variance reduction techniques have been developed to curb the instability, as well as, increase the simulation efficiencies of the Monte-Carlo methods. Our approach in this research work will consider the use of antithetic variate techniques to estimate the fair prices of barrier options. Next, we use the quasi-Monte Carlo method, together with Sobol sequence to estimate the values of the same option. An extended version of the Black-Scholes model will serve as basis for the exact prices of these exotic options. The resulting simulated prices will be compared to the exact prices. The research concludes by showing some results which proves that when random numbers are generated via low discrepancy sequences in contrast to the normal pseudo-random numbers, a more efficient simulation method is ensued. This is further applicable in pricing complex derivatives without closed formsolutions.

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Section: Introductionmentioning

confidence: 99%

A Comparative Study on Barrier Option Pricing using Antithetic and Quasi Monte-Carlo Simulations

Umeorah¹,

Mashele²

2018

Journal of Mathematics and Statistics

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Efficient exponential timestepping algorithm using control variate technique for simulating a functional of exit time of one-dimensional Brownian diffusion with applications in finance

Alzubaidi

2020

Arab. J. Math.

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The exponential timestepping Euler algorithm with a boundary test is adapted to simulate an expected of a function of exit time, such as the expected payoff of barrier options under the constant elasticity of variance (CEV) model. However, this method suffers from a high Monte Carlo (MC) statistical error due to its exponentially large exit times with unbounded samples. To reduce this kind of error efficiently and to speed up the MC simulation, we combine such an algorithm with an effective variance reduction technique called the control variate method. We call the resulting algorithm the improved Exp algorithm for abbreviation. In regard to the examples we consider in this paper for the restricted CEV process, we found that the variance of the improved Exp algorithm is about six times smaller than that of the Jansons and Lythe original method for the down-and-out call barrier option. It is also about eight times smaller for the up-and-out put barrier option, indicating that the gain in efficiency is significant without significant increase in simulation time.

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Randomized quasi Monte Carlo methods for pricing of barrier options under fractional Brownian motion

Murwaningtyas

Kartiko

Gunardi

et al. 2019

J. Phys.: Conf. Ser.

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Randomized quasi-Monte Carlo (RQMC) method is presented to compute the problem of a barrier option pricing. It is assumed that stock prices are modeled with a fractional Brownian motion (FBM). The FBM is a Gaussian process with dependent and stationary increments except H = ½. The FBM can model stock prices with short or long memory. We propose a trajectory generation technique based on fast Fourier transforms to simulate stock prices modeled by FBM. A stock price trajectory is utilized to predict pricing of barrier options. Barrier options are options whose payoff function depend on the stock prices during the option’s lifetime. Using the results of the stock price trajectory and RQMC method can be determined the price of a barrier option under FBM. We conclude that RQMC is an efficient technique for calculating the price of barrier options rather than a standard Monte Carlo (MC).

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Efficient Monte Carlo Algorithm Using Antithetic Variate and Brownian Bridge Techniques for Pricing the Barrier Options with Rebate Payments

Cited by 4 publications

References 18 publications

A Comparative Study on Barrier Option Pricing using Antithetic and Quasi Monte-Carlo Simulations

A Comparative Study on Barrier Option Pricing using Antithetic and Quasi Monte-Carlo Simulations

Efficient exponential timestepping algorithm using control variate technique for simulating a functional of exit time of one-dimensional Brownian diffusion with applications in finance

Randomized quasi Monte Carlo methods for pricing of barrier options under fractional Brownian motion

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