This paper examines the empirical validity of the deterministic volatility function (DVF) option valuation model, which assumes that the volatility of an asset's return is a deterministic function of the asset price and time. The authors use S&P 500 index option prices from June 1988 to December 1993 to evaluate the economic significance of the DVF model. They compare the predictive and hedging performance of the DVF model with an ad hoc Black-Scholes model with variable implied volatilities. The study finds that the DVF model performs worse than the ad hoc Black-Scholes model in terms of predictive accuracy and hedging performance. The authors also find that the implied volatility function is not stable over time, which undermines the reliability of the DVF model for valuation and risk management. They conclude that the Black-Scholes model, despite its constant volatility assumption, provides better results in practice. The paper highlights the "smile" and "sneer" patterns in implied volatilities, which indicate that the Black-Scholes model does not hold in financial markets. The authors argue that the volatility of asset returns is not constant but varies with the asset price and time. They also note that the DVF model, while theoretically sound, may overfit the data and fail to generalize well to new data. The study concludes that simpler models, such as the Black-Scholes model, are more reliable for practical applications. The authors suggest that future research should focus on generalizing the deterministic volatility framework and exploring alternative models for volatility. They also emphasize the importance of statistical testing for competing volatility structures and the need for further investigation into the implications of implied volatility patterns.This paper examines the empirical validity of the deterministic volatility function (DVF) option valuation model, which assumes that the volatility of an asset's return is a deterministic function of the asset price and time. The authors use S&P 500 index option prices from June 1988 to December 1993 to evaluate the economic significance of the DVF model. They compare the predictive and hedging performance of the DVF model with an ad hoc Black-Scholes model with variable implied volatilities. The study finds that the DVF model performs worse than the ad hoc Black-Scholes model in terms of predictive accuracy and hedging performance. The authors also find that the implied volatility function is not stable over time, which undermines the reliability of the DVF model for valuation and risk management. They conclude that the Black-Scholes model, despite its constant volatility assumption, provides better results in practice. The paper highlights the "smile" and "sneer" patterns in implied volatilities, which indicate that the Black-Scholes model does not hold in financial markets. The authors argue that the volatility of asset returns is not constant but varies with the asset price and time. They also note that the DVF model, while theoretically sound, may overfit the data and fail to generalize well to new data. The study concludes that simpler models, such as the Black-Scholes model, are more reliable for practical applications. The authors suggest that future research should focus on generalizing the deterministic volatility framework and exploring alternative models for volatility. They also emphasize the importance of statistical testing for competing volatility structures and the need for further investigation into the implications of implied volatility patterns.