GARCH vs. stochastic volatility: Option pricing and risk management

Abstract

This paper examines the out-of-sample performance of two common extensions of the Black-Scholes framework, namely a GARCH and a stochastic volatility option pricing model. The models are calibrated to intraday FTSE 100 option prices. We apply two sets of performance criteria, namely out-of-sample valuation errors and Value-at-Risk oriented measures. When we analyze the t to observed prices, GARCH clearly dominates both stochastic volatility and the benchmark Black S c holes model. However, the predictions of the market risk from hypothetical derivative positions show sizable errors. The t to the realized pro ts and losses is poor and there are no notable di erences between the models. Overall we therefore observe that the more complex option pricing models can improve on the Black S c holes methodology only for the purpose of pricing, but not for the Value-at-Risk forecasts.

Empirical Performance of Black-Scholes and GARCH Option Pricing Models during Turbulent Times: The Indian Evidence

“…Our second finding is that the GARCH model is free of the moneyness and maturity biases exhibited by the BSM model as demonstrated by orthogonality tests. This result in is in line with that of Lehar et al (2002) and Hsieh and Ritchken (2000).…”

“…Finally in line with existing research (Madan, Carr, & Chang, 1998;Lehar et al, 2002) we have conducted orthogonality tests to ascertain to what extent the GARCH model is able to address the pricing biases inherent in the BSM model. According to Madan et al a pricing model is good if its pricing errors do not demonstrate any pattern and are not predictable.…”

“…They concluded that the pricing performance of the GARCH model was better during the volatile period. Lehar, Schittenkopf and Scheicher (2002) compared the GARCH and Hull-White stochastic volatility model with the benchmark BSM model and found that the GARCH model fared better than the other two models in terms of pricing performance. However the performance of all three models in forecasting the www.ccsenet.org/ijef International Journal of Economics and Finance Vol.…”

Compare Value at Risk and Return of Assets Portfolio Stock, Gold, REIT, U.S. & Iran Market Indices

“…Lehar et al discover that more complex volatility models (GARCH and Stochastic volatility) are unable to progress on constant volatility models for VaR estimate, although they use for option pricing (Lehar et al, 2002). According to Brooks and Persaud, the relation performance of different models depends on the loss function used.…”

Jump Starting GARCH: Pricing and Hedging Options with Jumps in Returns and Volatilities

“…Heynen, Kemna and Vorst (1994), Duan (1996), Hardle and Hafner (2000), Heston and Nandi (2000), Hsieh and Ritchken (2000), Duan and Zhang (2001), Lehar, Scheicher and Schittenkopf (2002), Lehnert (2003) and Stentoft (2003) are some examples. More recently, examined a set of GARCH option models using the more general GARCH specifications given in Ding, Granger and Engle (1993) and Hentschel (1995).…”