Applications of Malliavin calculus to Monte Carlo methods in finance

Fournié, Éric; Lasry, Jean-Michel; Lebuchoux, Jérôme; Lions, Pierre-Louis; Touzi, Nizar

doi:10.1007/s007800050068

Cited by 442 publications

(551 citation statements)

References 16 publications

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“…The first sections of Chapter 4 follows the same steps as in Fournie et al (1999) to derive weights for what is known as rho, delta and vega in our generalised setting. This setting gives rise to two additional Greeks, for which stochastic weights also are derived, namely the sensitivities to jump intensity and jump am-plitude.…”

Section: Outline Of Thesismentioning

confidence: 99%

“…The treatment follows that of Fournie et al (1999), but in our more general setting of separable jump diffusions.…”

Section: Sensitivity Weightsmentioning

confidence: 99%

“…We rely heavily on the chain rule and the Skorohod integral, which allow us to repeat the steps in Fournie et al (1999).…”

Section: Variations In Tlie Initial Conditionmentioning

confidence: 99%

“…The fact that the class of continuously differentiable functions with bounded gradient is dense in can be used, exactly as in Fournie et al (1999), to prove the general result for cp & L^.…”

Section: Vv{x)mentioning

confidence: 99%

“…To overcome the deficiency of knowing the density explicitly Fournie et al (1999) introduced stochastic weights derived using Malliavin calculus rather than where tt is a random variable.…”

Section: Introductionmentioning

confidence: 99%

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Malliavin Calculus for Lévy Processes with Applications to Finance

Nunno¹,

Øksendal²,

Proske³

2009

317

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Section: Outline Of Thesismentioning

confidence: 99%

“…The treatment follows that of Fournie et al (1999), but in our more general setting of separable jump diffusions.…”

Section: Sensitivity Weightsmentioning

confidence: 99%

“…We rely heavily on the chain rule and the Skorohod integral, which allow us to repeat the steps in Fournie et al (1999).…”

Section: Variations In Tlie Initial Conditionmentioning

confidence: 99%

Section: Vv{x)mentioning

confidence: 99%

“…To overcome the deficiency of knowing the density explicitly Fournie et al (1999) introduced stochastic weights derived using Malliavin calculus rather than where tt is a random variable.…”

Section: Introductionmentioning

confidence: 99%

See 3 more Smart Citations

Malliavin Calculus for Lévy Processes with Applications to Finance

Nunno¹,

Øksendal²,

Proske³

2009

317

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Monte Carlo Greeks

Curran

2010

Encyclopedia of Quantitative Finance

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Sensitivity Computations: Integration by Parts

Chen

2010

Encyclopedia of Quantitative Finance

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Derivative price sensitivities, or greeks, play an important role in the practice of risk management to quantify the potential effects of the changes of underlying market parameters on the values of derivatives. However, how to calculate them efficiently is a challenging problem for computational finance. An obvious approach is to simulate replications of the model at perturbed parameters and then to use finite difference to form estimators. While this method has its own merits depending on the circumstances, it usually yields estimators with often unacceptably high variances, unless major computational efforts are made in terms of long calculation times. To obtain estimators with lower variance, traditional methods either differentiate the payoff functions of derivatives or differentiate the probability density of the underlying price. The former approach fails when the payoff functions are discontinuous while the latter meets difficulty if the explicit form of the density is not available. The integration‐by‐parts method overcomes both shortcomings of the traditional methods. It shifts the differential operator from the payoffs to the underlying diffusions in order to remove the smoothness requirement on the payoff functions. This method can be traced back to the Malliavin calculus in the field of stochastic analysis.

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Applications of Malliavin calculus to Monte Carlo methods in finance

Cited by 442 publications

References 16 publications

Malliavin Calculus for Lévy Processes with Applications to Finance

Malliavin Calculus for Lévy Processes with Applications to Finance

Monte Carlo Greeks

Sensitivity Computations: Integration by Parts

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