# Note on Valuation of Options Using @Risk

2 Pages Posted: 21 Oct 2008

See all articles by Robert M. Conroy

## Robert M. Conroy

University of Virginia - Darden School of Business

### Abstract

This brief technical note explains how to set up a Monte Carlo simulation using @Risk for the purpose of valuing options. It should be used in conjunction with the Excel spreadsheet UVA-F-1229X.

Excerpt

UVA-F-1229

Rev. Jun. 11, 2012

NOTE ON VALUATION OF OPTIONS USING @RISK

It is possible to use @Risk to value options. The approach is a Monte Carlo simulation. Stock prices are simulated and the payoff from the option for a particular price path is calculated and then discounted at the risk-free rate. After a number of trials, the mean of all the simulated present values is calculated as an estimate of the value of the option. A vast amount of the literature deals with this approach to option pricing. The purpose of this note is to provide a simple demonstration of this approach. The spreadsheet file, UVA-F-1229X, should be used in conjunction with this note. The file contains a simple @Risk model. This note is very brief as it assumes that all students are familiar with the basics of using Monte Carlo simulations on @Risk.

The key to creating a Monte Carlo simulation for option pricing is to estimate the price of the underlying stock at the maturity of the option. Once this is done, we can estimate the payoff value of the option. For demonstration purposes, let's consider a European call option with a one-year maturity: current stock price = \$ 10, exercise price = \$ 8, risk-free rate = 5% and volatility = 0.20. Based on the assumptions of lognormality of stock prices, S, the price at time t + 1, will be a function of the price at time t in the following manner:

St+1 = St + St(rf Dt + sZ),

. . .

Keywords: option valuation, Monte Carlo simulation

Suggested Citation

Conroy, Robert M., Note on Valuation of Options Using @Risk. Darden Case No. UVA-F-1229, Available at SSRN: https://ssrn.com/abstract=1279270

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