Implied Volatility and the Risk-Free Rate of Return in Options Markets

North American Journal of Economics and Finance, 31, 2015

40 Pages Posted: 29 Jan 2014 Last revised: 1 May 2015

Date Written: January 27, 2014

Abstract

This 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.

Keywords: re-pricing options, forecasting volatility, seemingly unrelated regression, implied volatility

JEL Classification: G13, C63

Suggested Citation

Bianconi, Marcelo and MacLachlan, Scott and Sammon, Marco, Implied Volatility and the Risk-Free Rate of Return in Options Markets (January 27, 2014). North American Journal of Economics and Finance, 31, 2015. Available at SSRN: https://ssrn.com/abstract=2386017 or http://dx.doi.org/10.2139/ssrn.2386017

Marcelo Bianconi (Contact Author)

Tufts University - Department of Economics ( email )

Medford, MA 02155
United States
617-627-2677 (Phone)

HOME PAGE: http://www.tufts.edu/~mbiancon

Scott MacLachlan

Tufts University ( email )

Medford, MA 02155
United States

Marco Sammon

Kellogg School of Management - Department of Finance ( email )

Evanston, IL 60208
United States

HOME PAGE: http://marcosammon.com/

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