Assessing the Least Squares Monte-Carlo Approach to American Option Valuation

Stentoft, Lars

doi:10.1023/b:redr.0000031176.24759.e6

Cited by 98 publications

(83 citation statements)

References 21 publications

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“…A detailed analysis of different orthogonal families is available in Stentoft (2004). Empirically, basis choice has only a mild effect on numerical precision, but strongly affects the variance of the algorithm.…”

Section: Numerical Methodmentioning

confidence: 99%

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Valuation of energy storage: an optimal switching approach

Carmona

Ludkovski

2010

Quantitative Finance

146

119

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We consider the valuation of energy storage facilities within the framework of stochastic control. Our two main examples are natural gas dome storage and hydroelectric pumped storage. Focusing on the timing flexibility aspect of the problem we construct an optimal switching model with inventory. Thus, the manager has a constrained compound American option on the inter-temporal spread of the commodity prices.Extending the methodology from Carmona and Ludkovski (2008), we then construct a robust numerical scheme based on Monte Carlo regressions. Our simulation method can handle a generic Markovian price model and easily incorporates many operational features and constraints. To overcome the main challenge of the path-dependent storage levels two numerical approaches are proposed. The resulting scheme is compared to the traditional quasi-variational framework and illustrated with several concrete examples. We also consider related problems of interest, such as supply guarantees and mines management.Key words : gas storage; optimal switching; least squares Monte Carlo; hydro pumped storage; impulse control, commodity derivatives AcknowledgmentsWe thank the participants of the Banff BIRS Workshop 07w-5502 "Mathematics and the Environment" and Zhenwei J. Qin for many useful comments and discussions. We also thank the anonymous referees whose feedback led to much improved presentation.

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Section: Numerical Methodmentioning

confidence: 99%

“…Nevertheless, extensive empirical experiments (Stentoft 2004) have strongly supported the general TvR/LSM methodology.…”

Section: Convergencementioning

confidence: 99%

Valuation of energy storage: an optimal switching approach

Carmona

Ludkovski

2010

Quantitative Finance

146

119

View full text Add to dashboard Cite

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“…The payoff at step j is then g j (X j ) = exp(−0.05t j ) max(0, K − X j ), where K = 101 is the strike price. For LSM, the basis functions are simple polynomials, as recommended by Stentoft (2004a), up to order 4: ψ 1 (x) = 1 and ψ k (x) = (x − 101) k−1 for k = 2, . .…”

Section: A Simple American Putmentioning

confidence: 99%

“…A good choice of basis functions can be very difficult in high dimensions, convergence is rather slow, and the approximate price is a biased estimator of the true price. The choice of basis functions is studied empirically by Stentoft (2004a). For a given set of basis functions, the accuracy can be improved by using variance reduction methods, such as control variates, importance sampling, and randomized quasi-Monte Carlo (RQMC), for example.…”

Section: Introductionmentioning

confidence: 99%

American option pricing with randomized quasi-Monte Carlo simulations

Dion

L’Ecuyer

2010

Proceedings of the 2010 Winter Simulation Conference

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We study the pricing of American options using least-squares Monte Carlo combined with randomized quasi-Monte Carlo (RQMC), viewed as a variance reduction method. We find that RQMC reduces both the variance and the bias of the option price obtained in an out-of-sample evaluation of the retained policy, and improves the quality of the returned policy on average. Various sampling methods of the underlying stochastic processes are compared and the variance reduction is analyzed in terms of a functional ANOVA decomposition.

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“…Papers focusing on theoretical aspects include: the property of the price function such as differentiability, convexity, and put-call symmetry (Bergman, Grundy and Wiener (1996), McDonald andSchroder (1998), Shroder (1999)); the property of the critical stock price boundary (van Moerbeke (1976), Barles, Burdeau, Romano and Samsoen (1995), Peskir (2005), Zhu (2006); different formulations such as partial differential equation with free boundary (McKean (1965)), optimal stopping problem and its dual formulation (Bensoussan (1984), Karatzas (1988), Rogers (2002)), variational inequality (Jaillet, Lamberton and Lapeyre (1990)), and early exercise premium representation (Kim (1990), Jacka (1991), Carr, Jarrow and Myneni (1992)); 1 convergence and other properties of numerical methods (Lamberton (1993(Lamberton ( , 1998, Amin and Khanna (1994), Clément, Lamberton, and Protter (2002), Stentoft (2004)); and finally various generalizations such as general diffusion processes (Detemple and Tian (2002)), multiple underlying assets (Detemple, Feng and Tian (2003)), and more exotic American-type derivatives (see Detemple (2006)). …”

Section: Introductionmentioning

confidence: 99%

A quasi-analytical interpolation method for pricing American options under general multi-dimensional diffusion processes

2009

Rev Deriv Res

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We present a quasi-analytical method for pricing multi-dimensional American options based on interpolating two arbitrage bounds, along the lines of Johnson (1983). Our method allows for the close examination of the interpolation parameter on a rigorous theoretical footing instead of empirical regression. The method can be adapted to general diffusion processes as long as quick and accurate pricing methods exist for the corresponding European and perpetual American options. The American option price is shown to be approximately equal to an interpolation of two European option prices with the interpolation weight proportional to a perpetual American option. In the Black-Scholes model, our method achieves the same efficiency as Barone-Adesi and Whaley's (1987) quadratic approximation with our method being generally more accurate for out-of-the-money and long-maturity options. When applied to Heston's stochastic volatility model, our method is shown to be extremely efficient and fairly accurate.

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Assessing the Least Squares Monte-Carlo Approach to American Option Valuation

Cited by 98 publications

References 21 publications

Valuation of energy storage: an optimal switching approach

Valuation of energy storage: an optimal switching approach

American option pricing with randomized quasi-Monte Carlo simulations

A quasi-analytical interpolation method for pricing American options under general multi-dimensional diffusion processes

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