## Mark Broadie

### “Exact Simulation of Option Greeks Under Stochastic Volatility and Jump Diffusion Models”

Coauthor(s): O. Kaya.

Editors: R. G. Ingalls, M. D. Rossetti, J. S. Smith, and B. A. Peters

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**Abstract:**

This paper derives Monte Carlo simulation estimators to compute
option price derivatives, i.e., the `Greeks,' under Heston's
stochastic volatility model and some variants of it which include
jumps in the price and variance processes. We use pathwise and
likelihood ratio approaches together with the exact simulation method
of Broadie and Kaya (2004) to generate unbiased estimates of option
price derivatives in these models. By appropriately conditioning on
the path generated by the variance and jump processes, the evolution
of the stock price can be represented as a series of lognormal random
variables. This makes it possible to extend previously known results
from the Black-Scholes setting to the computation of Greeks for
more complex models. We give simulation estimators and numerical
results for some path-dependent and path-independent options.

**Source:** *Proceedings of the 2004 Winter Simulation Conference*

**Exact Citation:**

Broadie, Mark, and O. Kaya. "Exact Simulation of Option Greeks Under Stochastic Volatility and Jump Diffusion Models." In *Proceedings of the 2004 Winter Simulation Conference*, 1607-15. Ed. R. G. Ingalls, M. D. Rossetti, J. S. Smith, and B. A. Peters. Washington: INFORMS, 2004.

**Pages:** 1607-15

**Place:** Washington

**Date:**
2004