Home About Latest Browse RSS Advanced Search

Federal Reserve Bank of Atlanta
FRB Atlanta Working Paper
A closed-form GARCH option pricing model
Steven L. Heston
Saikat Nandi

This paper develops a closed-form option pricing formula for a spot asset whose variance follows a GARCH process. The model allows for correlation between returns of the spot asset and variance and also admits multiple lags in the dynamics of the GARCH process. The single-factor (one-lag) version of this model contains Heston's (1993) stochastic volatility model as a diffusion limit and therefore unifies the discrete-time GARCH and continuous-time stochastic volatility literature of option pricing. The new model provides the first readily computed option formula for a random volatility model in which current volatility is easily estimated from historical asset prices observed at discrete intervals. Empirical analysis on S&P 500 index options shows the single-factor version of the GARCH model to be a substantial improvement over the Black-Scholes (1973) model. The GARCH model continues to substantially outperform the Black-Scholes model even when the Black-Scholes model is updated every period and uses implied volatilities from option prices, while the parameters of the GARCH model are held constant and volatility is filtered from the history of asset prices. The improvement is due largely to the ability of the GARCH model to describe the correlation of volatility with spot returns. This allows the GARCH model to capture strike-price biases in the Black-Scholes model that give rise to the skew in implied volatilities in the index options market.

Download Full text
Cite this item
Steven L. Heston & Saikat Nandi, A closed-form GARCH option pricing model, Federal Reserve Bank of Atlanta, FRB Atlanta Working Paper 97-9, 1997.
More from this series
JEL Classification:
Subject headings:
Keywords: Econometric models ; Financial markets ; Options (Finance) ; Prices
For corrections, contact Elaine Clokey ()
Fed-in-Print is the central catalog of publications within the Federal Reserve System. It is managed and hosted by the Economic Research Division, Federal Reserve Bank of St. Louis.

Privacy Legal