Working Paper: CEPR ID: DP1369
Authors: Bernard Dumas; Jeff Fleming; Robert E. Whaley
Abstract: Black and Scholes (1973) implied volatilities tend to be systematically related to the option?s exercise price and time to expiration. Derman and Kani (1994), Dupire (1994), and Rubinstein (1994) attribute this behaviour to the fact that the Black/Scholes constant volatility assumption is violated in practice. These authors hypothesize that the volatility of the underlying asset?s return is a deterministic function of the asset price and time, and develop the deterministic volatility function (DVF) option valuation model, which has the potential of fitting the observed cross-section of option prices exactly. Using a sample of Standard and Poors index of 500 companies (S&P 500) options during the period June 1988 through December 1993, we evaluate the economic significance of the implied deterministic volatility function by examining the predictive and hedging performance of the DVF option valuation model.
Keywords: Asset Prices; Volatility
JEL Codes: G13
Edges that are evidenced by causal inference methods are in orange, and the rest are in light blue.
| Cause | Effect |
|---|---|
| Deterministic Volatility Function (DVF) (C69) | Option Pricing (G13) |
| Black-Scholes model's constant volatility assumption (C58) | Systematic variations in implied volatility (C69) |
| Asset Price (G19) | Volatility of Returns (G17) |
| Time to Expiration decreases (C41) | Implied Volatilities exhibit a 'sneer' pattern (E32) |
| DVF model's predictive performance deteriorates over time (C22) | Estimated volatility function is not stable (C69) |
| Simpler models (including Black-Scholes) (C29) | Better predictions and hedging performance than DVF model (G17) |