Approximating American option prices in the GARCH framework

Duan, Jin‐Chuan; Gauthier, Geneviève; Sasseville, Caroline; Simonato, Jean‐Guy

doi:10.1002/fut.10096

Cited by 13 publications

(5 citation statements)

References 18 publications

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“…Examples of calculations are provided for the case of an American call-on-max option on one and two assets. The second example is the N-GARCH model, as studied in Duan and Simonato (2001) and Duan et al (2003). Examples of calculations are given for the American put option.…”

Section: Implementation Issuesmentioning

confidence: 99%

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Monte Carlo Approximations of American Options that Preserve Monotonicity and Convexity

Moral

Rémillard

Rubenthaler³

2012

Springer Proceedings in Mathematics

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It can be shown that when the payoff function is convex and decreasing (respectively increasing) with respect to the underlying (multidimensional) assets, then the same is true for the value of the associated American option, provided some conditions are satisfied. In such a case, all Monte Carlo methods proposed so far in the literature do not preserve the convexity or monotonicity properties. In this paper, we propose a method of approximation for American options which can preserve both convexity and monotonicity. The resulting values can then be used to define exercise times and can also be used in combination with primal-dual methods to get sharper bounds. Other application of the algorithm include finding optimal hedging strategies. Recently, two-stage Monte Carlo methods were developed by Rogers (2002), Andersen and Broadie (2004) and Haugh and Kogan (2004). For an interesting review of Monte Carlo methods, see Fu et al. (2001).

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Section: Implementation Issuesmentioning

confidence: 99%

“…In Duan and Simonato (2001) and Duan et al (2003), the authors proposed two kinds of approximations for the American put option on S k . They calculated the option prices for Table 3.…”

Section: Geometric Brownian Motionmentioning

confidence: 99%

Monte Carlo Approximations of American Options that Preserve Monotonicity and Convexity

Moral

Rémillard

Rubenthaler³

2012

Springer Proceedings in Mathematics

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“…Duan and Simonato (2001) propose an approximation of the GARCH process by a finite-state Markov chain with two state variables; and Duan et al (2003) propose using analytical approximations to reduce the dimensionality of a binomial tree from 2 to 1. Stentoft (2005) adapts the Least Squares Monte Carlo method of Longstaff and Schwartz (2001) to value American put options.…”

Section: Introductionmentioning

confidence: 99%

Option Pricing Under GARCH Processes Using PDE Methods

Breton

Frutos

2010

Operations Research

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In this paper, we propose a partial differential equation formulation for the value of an option when the underlying asset price is described by a discrete-time GARCH process. Our numerical approach involves a spectral Fourier-Chebyshev interpolation. Numerical illustrations are provided, and the results are compared with other available valuation methods. Our numerical procedure converges exponentially fast and allows for the efficient computation of option prices, achieving a high level of precision in a few seconds of computing time.

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“…A recombining implied binomial tree is then deduced using risk neutral principles to describe the asset price evolution over the life of the option contract. In Duan et al (2003), this approach is numerically shown to provide a useful and simple alternative for approximating the prices of American options in the GARCH framework. Although such an approach does not have the convergence property shared by other methods proposed in the literature, it represents a convenient alternative if computation time or memory requirement is an issue.…”

Section: Introductionmentioning

confidence: 99%

Johnson binomial trees

Simonato

2011

Quantitative Finance

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Rubinstein developed a binomial lattice technique for pricing European and American derivatives in the context of skewed and leptokurtic asset return distributions. A drawback of this approach is the limited set of skewness and kurtosis pairs for which valid stock return distributions are possible. A solution to this problem is proposed here by extending Rubinstein's Edgeworth tree idea to the case of the Johnson system of distributions which is capable of accommodating all possible skewness and kurtosis pairs. Numerical examples showing the performance of the Johnson tree to approximate the prices of European and American options in Merton's jump diffusion framework and Duan's GARCH framework are examined.Edgeworth binomial tree, Skewness, Kurtosis, Johnson distribution, American option, Jump diffusion, GARCH,

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Approximating American option prices in the GARCH framework

Cited by 13 publications

References 18 publications

Monte Carlo Approximations of American Options that Preserve Monotonicity and Convexity

Monte Carlo Approximations of American Options that Preserve Monotonicity and Convexity

Option Pricing Under GARCH Processes Using PDE Methods

Johnson binomial trees

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