Skip to main content
Article thumbnail
Location of Repository

Sensitivity analysis for averaged asset price dynamics with gamma processes

By Reiichiro Kawai and Atsushi Takeuchi

Abstract

The main purpose of this paper is to derive unbiased Monte Carlo estimators of various sensitivity indices for an averaged asset price dynamics governed by the gamma Lévy process. The key idea is to apply a scaling property of the gamma process with respect to the Esscher density transform parameter. Our framework covers not only the continuous Asian option, but also European, discrete Asian, average strike Asian, weighted average, spread options, and geometric average Asian options. Numerical results are provided to illustrate the effectiveness of our formulas in Monte Carlo simulations, relative to finite difference approximation

Topics: Asian options, Esscher transform, gamma process, Greeks, Lévy process, Malliavin calculus
Publisher: Elsevier
Year: 2010
DOI identifier: 10.1016/j.spl.2009.09.010
OAI identifier: oai:lra.le.ac.uk:2381/7625
Journal:

Suggested articles

Citations

  1. (2010). 80(1) 42-49. ¤Email Eddress: reiichiro.kawai@gmail.com. Postal Address: Department of Mathematics, University of Leicester, Leicester LE1 7RH, UK. †Corresponding Author. Email Address: takeuchi@sci.osaka-cu.ac.jp. Postal Address:
  2. (1999). Applications of Malliavin calculus to Monte Carlo methods in finance. doi
  3. (1983). Calcul des variations stochastique et processus de sauts. doi
  4. (2009). Computation of Greeks and multidimensional density estimation for asset price models with time-changed Brownian motion, to appear in doi
  5. (2004). Computations of Greeks in a market with jumps via the Malliavin calculus. doi
  6. (1990). Differential calculus and integration by parts on Poisson space, doi
  7. (2009). Greeks formulae for an asset price model with gamma processes, under revision. doi
  8. (2007). Integration by parts formula for locally smooth laws and applications to sensitivity computations, doi
  9. (1987). Malliavin calculus for processes with jumps, doi
  10. (2006). Malliavin Monte Carlo Greeks for jump diffusions. Stochastic Process. doi
  11. (1999). Option pricing and the fast Fourier transform. doi
  12. (1998). Processes of normal inverse Gaussian type. doi
  13. (2003). Stochastic Volatility for Le´vy processes. doi
  14. (2007). The Bismut-Elworthy-Li formula for jump-diffusions and applications to Monte Carlo methods in finance, available at arXiv:math/0604311v3.
  15. (2009). The Bismut-Elworthy-Li type formulae for stochastic differential equations with jumps, under revision. doi
  16. (1997). The normal inverse Gaussian Le´vy process: simulation and approximation. doi
  17. (1998). The variance gamma process and option pricing. doi

To submit an update or takedown request for this paper, please submit an Update/Correction/Removal Request.