American options under stochastic volatility: control variates, maturity randomization & multiscale asymptotics

Agarwal, A. , Juneja, S. and Sircar, R. (2016) American options under stochastic volatility: control variates, maturity randomization & multiscale asymptotics. Quantitative Finance, 16(1), pp. 17-30. (doi:10.1080/14697688.2015.1068443)

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Abstract

American options are actively traded worldwide on exchanges, thus making their accurate and efficient pricing an important problem. As most financial markets exhibit randomly varying volatility, in this paper we introduce an approximation of American option price under stochastic volatility models. We achieve this by using the maturity randomization method known as Canadization. The volatility process is characterized by fast and slow scale fluctuating factors. In particular, we study the case of an American put with a single underlying asset and use perturbative expansion techniques to approximate its price as well as the optimal exercise boundary up to the first order. We then use the approximate optimal exercise boundary formula to price American put via Monte Carlo. We also develop efficient control variates for our simulation method using martingales resulting from the approximate price formula. A numerical study is conducted to demonstrate that the proposed method performs better than the least squares regression method popular in the financial industry, in typical settings where values of the scaling parameters are small. Further, it is empirically observed that in the regimes where scaling parameter value is equal to unity, fast and slow scale approximations are equally accurate.

Item Type:Articles
Status:Published
Refereed:Yes
Glasgow Author(s) Enlighten ID:Agarwal, Dr Ankush
Authors: Agarwal, A., Juneja, S., and Sircar, R.
Subjects:H Social Sciences > HG Finance
Q Science > QA Mathematics
College/School:College of Social Sciences > Adam Smith Business School > Economics
Journal Name:Quantitative Finance
Publisher:Taylor & Francis
ISSN:1469-7688
ISSN (Online):1469-7696
Published Online:06 August 2015
Copyright Holders:Copyright © 2015 Taylor and Francis
First Published:First published in Quantitative Finance 16(1): 17-30
Publisher Policy:Reproduced in accordance with the publisher copyright policy

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