Malliavin Greeks without Malliavin Calculus
نویسندگان
چکیده
We derive and analyze Monte Carlo estimators of price sensitivities (“Greeks”) for contingent claims priced in a diffusion model. There have traditionally been two categories of methods for estimating sensitivities: methods that differentiate paths and methods that differentiate densities. A more recent line of work derives estimators through Malliavin calculus. The purpose of this article is to investigate connections between Malliavin estimators and the more traditional and elementary pathwise method and likelihood ratio method. Malliavin estimators have been derived directly for diffusion processes, but implementation typically requires simulation of a discrete-time approximation. This raises the question of whether one should discretize first and then differentiate, or differentiate first and then discretize. We show that in several important cases the first route leads to the same estimators found through Malliavin calculus, but using only elementary techniques. Time-averaging of multiple estimators emerges as a key feature in achieving convergence to the continuous-time limit.
منابع مشابه
Malliavin Calculus in Finance
This article is an introduction to Malliavin Calculus for practitioners. We treat one specific application to the calculation of greeks in Finance. We consider also the kernel density method to compute greeks and an extension of the Vega index called the local vega index.
متن کاملMalliavin Calculus for Markov Chains using Perturbations of Time
In this article, we develop a Malliavin calculus associated to a timecontinuous Markov chain with finite state space. We apply it to get a criterion of density for solutions of SDE involving the Markov chain and also to compute greeks. keywords: Dirichlet form; Integration by parts formula; Malliavin calculus; Markov chain; computation of greeks. Mathematics subject classification: 60H07; 60J10...
متن کاملEfficient simulation of Greeks of multiasset European and Asian style options by Malliavin calculus and quasi-Monte Carlo methods
Keywords: Multiasset options Option sensitivities or Greeks Malliavin calculus Monte Carlo and quasi-Monte Carlo methods a b s t r a c t This paper discusses simulation of sensitivities or Greeks of multiasset European and Asian style options by Malliavin calculus combined with Monte Carlo and quasi-Monte Carlo methods. By using the Malliavin calculus, we are able to express Greeks of both Euro...
متن کاملMalliavin Calculus applied to Finance
In this article, we give a brief informal introduction to Malliavin Calculus for newcomers. We apply these ideas to the simulation of Greeks in Finance. First to European-type options where formulas can be computed explicitly and therefore can serve as testing ground. Later we study the case of Asian options where close formulas are not available, and we also open the view for including more ex...
متن کامل