Prices and sensitivities of Asian options: A survey

Boyle, Phelim; Potapchik, Alexander

doi:10.1016/j.insmatheco.2007.02.003

Cited by 58 publications

(45 citation statements)

References 51 publications

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“…In this paper we restrict ourself to expose the estimators values and invite the reader to consult [13] or [17] for more details. The pathwise method is based on the relationship between the security payoff and the parameter of interest.…”

Section: Pathwise Derivatives and Likelihood Ratios Methodsmentioning

confidence: 99%

“…Also, Boyle et al shows in [16] that in some cases the rate of convergence of this method is N −1/2 , especially through using common random numbers. Nevertheless, this method within the Monte Carlo framework suffer from two shortcomings: it is biased and they require multiple re-simulations [17]. Thus, we have two numerical errors, the first results from the use of finite difference approximations, while the second is related to the method of Monte Carlo.…”

Section: Finite Difference Approximationsmentioning

confidence: 99%

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Estimators of sensitivities of an Asian option: numerical analysis

Moussi¹,

Lidouh²,

Nqi³

2014

ijma

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Section: Pathwise Derivatives and Likelihood Ratios Methodsmentioning

confidence: 99%

Section: Finite Difference Approximationsmentioning

confidence: 99%

Estimators of sensitivities of an Asian option: numerical analysis

Moussi¹,

Lidouh²,

Nqi³

2014

ijma

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show abstract

“…A survey of current methods up to 2006 for pricing Asian options and computing their sensitivities to the key input parameters is provided in Boyle and Potapchik (2008). The methods discussed there include also the comonotonic bounds.…”

Section: Applications Of the Theory Of Comonotonicity 41 Derivativesmentioning

confidence: 99%

Advanced Mathematical Methods for Finance

Nunno¹,

Øksendal²

2011

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Over the last decade, it has been shown that the concept of comonotonicity is a helpful tool for solving several research and practical problems in the domain of finance and insurance. In this paper, we give an extensive bibliographic overview -without claiming to be complete -of the developments of the theory of comonotonicity and its applications, with an emphasis on the achievements over the last five years. These applications range from pricing and hedging of derivatives over risk management to life insurance. ComonotonicityOver the last two decades, researchers in economics, financial mathematics and actuarial science have introduced results related to the concept of comonotonicity in their respective fields of interest. In this paper, we give an overview of the relevant literature in these research fields, with the main emphasis on the development of the theory and its applications in finance and insurance over the last five years. Although it is our intention to give an extensive bibliographic overview, due to the high number of papers on applications of comonotonicity, it is impossible to present here an exhaustive overview of the recent literature. Further, we restrict this paper to a description of how and where comonotonicity comes in and refer to the relevant papers for a detailed mathematical description. In order to make this paper self-contained, we also provide a short overview of the basic definitions and initial main results of comonotonicity theory, hereby referring to part of the older literature on this topic.The concept of comonotonicity is closely related to the following well-known result, which is usually attributed to both Hoeffding (1940) and Fréchet (1951): For any n-dimensional random vector X ≡ (X 1 , X 2 , . . . , X n ) with multivariate cumulative distribution function (cdf) F X and marginal univariate cdf's F X 1 , F X 2 , . . . , F Xn and for any x ≡ (x 1 , x 2 , . . . , x n ) ∈ R n it holds that F X (x) ≤ min (F X 1 (x 1 ) , F X 2 (x 2 ) , . . . , F Xn (x n )) .(1)In the sequel, the notation R n (F X 1 , F X 2 , . . . , F Xn ) will be used to denote the class of all random vectors Y ≡ (Y 1 , Y 2 , . . . , Y n ) with marginals F Y i equal to the respective marginals F X i . The set R n (F X 1 , F X 2 , . . . , F Xn ) is called the Fréchet class related to the random vector X.The upper bound in (1) is reachable in the Fréchet class R n (F X 1 , F X 2 , . . . , F Xn ) in the sense that it is the cdf of an n-dimensional random vector with marginals given by F X i , i = 1, 2, . . . , n. * Department of Mathematics, ECARES, Université Libre de Bruxelles, CP 210, 1050 Brussels, Belgium † Faculty of Business and Economics, Katholieke Universiteit, 3000 Leuven, Belgium. ‡ Department of Applied Mathematics and Computer Science, Ghent University, Krijgslaan 281 S9, 9000 Gent, Belgium 1 In order to prove the reachability property, consider a random variable U , uniformly distributed on the unit interval (0, 1). Then one has that F −1 X 1 (U ), F −1 X 2 (U ), . . . , F −1 Xn (U ) ∈ ...

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“…On the other hand, further numerical procedures addressing either Monte Carlo simulation or various approximations of Asian options have been studied by Kemna and Vorst [12], Turnbull and Wakeman [20], Rogers and Shi [18], and Simon, Goovaerts, and Dhaene [19] to mention only a few. For a more comprehensive literature review we refer to the excellent survey article of Boyle and Potapchik [2].…”

Section: Introductionmentioning

confidence: 99%

Pricing and Hedging of Asian Options: Quasi-Explicit Solutions via Malliavin Calculus

2011

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We use Malliavin calculus and the Clark-Ocone formula to derive the hedging strategy of an arithmetic Asian Call option in general terms. Furthermore we derive an expression for the density of the integral over time of a geometric Brownian motion, which allows us to express hedging strategy and price of the Asian option as an analytic expression. Numerical computations which are based on this expression are provided.

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Prices and sensitivities of Asian options: A survey

Cited by 58 publications

References 51 publications

Estimators of sensitivities of an Asian option: numerical analysis

Estimators of sensitivities of an Asian option: numerical analysis

Advanced Mathematical Methods for Finance

Pricing and Hedging of Asian Options: Quasi-Explicit Solutions via Malliavin Calculus

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