Implied Volatility and the Risk-Free Rate of Return in Options Markets
AbstractThis paper implements an algorithm that can be used to solve systems of Black-Scholes equations for implied volatility and implied risk-free rate of return. After using a seemingly unrelated regressions (SUR) model to obtain point estimates for implied volatility and implied risk-free rate, the options are re-priced using these parameters in the Black-Scholes formula. Given this re-pricing, we find that the difference between the market and model price is increasing in moneyness, and decreasing in time to expiration and the size of the bid ask spread. We ask whether the new information gained by the simultaneous solution is useful. We find that after using the SUR model, and re-pricing the options, the varying risk-free rate model yields Black-Scholes prices closer to market prices than the fixed risk-free rate model. We also find that the varying risk-free rate model is better for predicting future evolutions in model-free implied volatility as measured by the VIX. Finally, we discuss potential trading strategies based both on the model-based Black-Scholes prices and on VIX predictability.
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Bibliographic InfoPaper provided by Department of Economics, Tufts University in its series Discussion Papers Series, Department of Economics, Tufts University with number 0777.
Date of creation: 2014
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re-pricing options; forecasting volatility; seemingly unrelated regression; implied volatility;
Find related papers by JEL classification:
- G13 - Financial Economics - - General Financial Markets - - - Contingent Pricing; Futures Pricing
- C63 - Mathematical and Quantitative Methods - - Mathematical Methods; Programming Models; Mathematical and Simulation Modeling - - - Computational Techniques
This paper has been announced in the following NEP Reports:
- NEP-ALL-2014-02-15 (All new papers)
- NEP-FOR-2014-02-15 (Forecasting)
- NEP-MST-2014-02-15 (Market Microstructure)
- NEP-SOG-2014-02-15 (Sociology of Economics)
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