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

被引:20
作者
Agarwal, Ankush [1 ]
Juneja, Sandeep [1 ]
Sircar, Ronnie [2 ]
机构
[1] Tata Inst Fundamental Res, Sch Technol & Comp Sci, Bombay 400005, Maharashtra, India
[2] Princeton Univ, ORFE Dept, Princeton, NJ 08544 USA
基金
美国国家科学基金会;
关键词
Stochastic volatility; American option; Maturity randomization; Singular perturbation theory; Regular perturbation theory; Monte Carlo; Control variate; SIMULATION;
D O I
10.1080/14697688.2015.1068443
中图分类号
F8 [财政、金融];
学科分类号
0202 ;
摘要
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 an 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 an 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 the scaling parameter value is equal to unity, fast and slow-scale approximations are equally accurate.
引用
收藏
页码:17 / 30
页数:14
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