LP valuation of exotic American options exploiting structure

Dempster, M. A. H.; Hutton, J.P.; Richards, David

doi:10.21314/jcf.1998.020

Cited by 39 publications

(27 citation statements)

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“…This also follows from applying to (15) and (17) the Euler-McLaurin formula lim T !1 c =T = = (1 + ), see Abramowitz and Stegun (1974). In particular, in the Gaussian case 2 we obtain that, under the appropriate measures, e Y is Normal with mean ln S 0 + m =2 and variance 2 =3, which is the result that appears in Hull (2005).…”

Section: [Insert Table (3) Here]mentioning

confidence: 92%

“…For the discrete case, Clewlow and Carverhill (1990), Andreasen (2002), Dempster et al (1998), Zvan et al (1999) focus their attention on the geometric Brownian motion. Benhamou (2002) enhances the algorithm of Clewlow and Carverhill (1990) based on a Fast Fourier technique and adapt it to some non-lognormal densities, like the Student t. Their approaches, although innovative, require computationally intensive numerical methods or approximations for which no clear error bound is available.…”

Section: Introductionmentioning

confidence: 99%

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Pricing Discretely Monitored Asian Options by Maturity Randomization

Fusai¹,

Marazzina²,

Marena³

2011

SIAM J. Finan. Math.

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We present methodologies to price discretely monitored Asian options when the underlying evolves according to a generic Lévy process. For geometric Asian options we provide closed-form solutions in terms of the Fourier transform and we study in particular these formulas in the Lévy-stable case. For arithmetic Asian options we solve the valuation problem by recursive integration and derive a recursive theoretical formula for the moments to check the accuracy of the results. We compare the implementation of our method to Monte Carlo simulation implemented with control variates and using di¤erent parametric Lévy processes. We also discuss model-risk issues.JEL Classi…cation: G13, C63

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Section: [Insert Table (3) Here]mentioning

confidence: 92%

Section: Introductionmentioning

confidence: 99%

Pricing Discretely Monitored Asian Options by Maturity Randomization

Fusai¹,

Marazzina²,

Marena³

2011

SIAM J. Finan. Math.

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“…Then discretizing equation (3.11) along the characteristic trajectory for different timestepping schemes gives, in the case of fully implicit timestepping: 14) and for Crank-Nicolson timestepping (CN),…”

Section: Semi-lagrangian Discretizationmentioning

confidence: 99%

A Semi-Lagrangian Approach for American Asian Options under Jump Diffusion

d’Halluin¹,

Forsyth²,

Labahn³

2005

SIAM J. Sci. Comput.

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A semi-Lagrangian method is presented to price continuously observed fixed strike Asian options. At each timestep a set of one dimensional partial integral differential equations (PIDEs) is solved and the solution of each PIDE is updated using semi-Lagrangian timestepping. Crank-Nicolson and second order backward differencing timestepping schemes are studied. Monotonicity and stability results are derived. With low volatility values, it is observed that the non-smoothness at the strike in the payoff affects the convergence rate; sub-quadratic convergence rate is observed.

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“…We chose to consider zero dividend and continuous average in order to not complicate the situation with discontinuities, apart from the ones otherwise provided by the problem itself, even though especially the discrete averages has attracted some attention in the last few years, see for example [3,4,5]. Further, we chose to consider a fixed strike (instead of a floating) and an arithmetic average (instead of a geometric) since these are the predominant in the market according to [6].…”

Section: C218mentioning

confidence: 99%

A fixed strike Asian option and comments on its numerical solution

Hugger¹

2004

ANZIAMJ

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A boundary value formulation of an Asian option is solved with a wide range of standard textbook explicit finite difference methods including also artificial diffusion methods. We investigate the dependence of the numerical methods on the various degeneracies and approximations in the boundary value formulation. It is concluded that numerical solutions are generally oscillatory, that a simple artificial diffusion approach does not resolve this problem, but that by selecting the appropriate methods, oscillations can be avoided.

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LP valuation of exotic American options exploiting structure

Cited by 39 publications

References 0 publications

Pricing Discretely Monitored Asian Options by Maturity Randomization

Pricing Discretely Monitored Asian Options by Maturity Randomization

A Semi-Lagrangian Approach for American Asian Options under Jump Diffusion

A fixed strike Asian option and comments on its numerical solution

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