## Mark Broadie

*Estimating Security Price Derivatives Using Simulation*

Coauthor(s): Paul Glasserman.

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**Abstract:**

Simulation has proved to be a valuable tool for estimating security prices for which simple closed form solutions do not exist. In this paper we present two direct methods, a pathwise method and a likelihood ratio method, for estimating derivatives of security prices using simulation. With the direct methods, the information from a single simulation can be used to estimate multiple derivatives along with a security's price. The main advantage of the
direct methods over re-simulation is increased computational speed. Another advantage is that the direct methods give unbiased estimates of derivatives, whereas the estimates obtained by re-simulation are biased. Computational results are given for both direct methods and comparisons are made to the standard method of re-simulation to
estimate derivatives. The methods are illustrated for a path independent model (European options), a path dependent model (Asian options), and a model with multiple state variables (options with stochastic volatility).

**Source:** *Management Science*

**Exact Citation:**

Broadie, Mark, and Paul Glasserman. "Estimating Security Price Derivatives Using Simulation." *Management Science* 42, no. 2 (1996): 269-85.

**Volume:** 42

**Number:** 2

**Pages:** 269-85

**Date:**
1996