Abstract

The aim of this study is to demonstrate a framework to model the implied volatilities of S&P 500 index options and estimate the implied volatilities of stock prices using stochastic processes. In this paper, three models are established to estimate whether the implied volatilities are constant during the whole life of options. We mainly concentrate on the Black-Scholes and Dumas’ option models and make the empirical comparisons. By observing the daily-recorded data of S&P 500 index, we study the volatility model and volatility surface. Results from numerical experiments show that the stochastic volatilities are determined by moneyness rather than constant. Our research is of vital importance, especially for forecasting stock market shocks and crises, as one of the applications.

Keywords:

Moneyness, out-of-the money options, parameters estimation, volatility surface,

References

Competing interests

The authors have no competing interests.

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Copyright

The authors have no competing interests.