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Implied volatility and the risk-free rate of return in options markets

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  • Bianconi, Marcelo
  • MacLachlan, Scott
  • Sammon, Marco

Abstract

We numerically solve systems of Black–Scholes formulas 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. After repricing, the difference between the market price and model price is increasing in time to expiration, while the effect of moneyness and the bid-ask spread are ambiguous. Our varying risk-free rate model yields Black–Scholes prices closer to market prices than the fixed risk-free rate model. In addition, our model is better for predicting future evolutions in model-free implied volatility as measured by the VIX.

Suggested Citation

  • Bianconi, Marcelo & MacLachlan, Scott & Sammon, Marco, 2015. "Implied volatility and the risk-free rate of return in options markets," The North American Journal of Economics and Finance, Elsevier, vol. 31(C), pages 1-26.
    • Handle: RePEc:eee:ecofin:v:31:y:2015:i:c:p:1-26
    DOI: 10.1016/j.najef.2014.10.003
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    Cited by:

    1. Magomet Yandiev, 2021. "Risk-Free Rate in the Covid-19 Pandemic: Application Mistakes and Conclusions for Traders," Papers 2111.07075, arXiv.org.
    2. Arısoy, Yakup Eser & Altay-Salih, Aslıhan & Akdeniz, Levent, 2015. "Aggregate volatility expectations and threshold CAPM," The North American Journal of Economics and Finance, Elsevier, vol. 34(C), pages 231-253.
    3. Wang, Ximei & Zhao, Yanlong & Bao, Ying, 2019. "Arbitrage-free conditions for implied volatility surface by Delta," The North American Journal of Economics and Finance, Elsevier, vol. 48(C), pages 819-834.
    4. Lin, Shin-Hung & Huang, Hung-Hsi & Li, Sheng-Han, 2015. "Option pricing under truncated Gram–Charlier expansion," The North American Journal of Economics and Finance, Elsevier, vol. 32(C), pages 77-97.

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    More about this item

    Keywords

    Re-pricing options; Forecasting volatility; Seemingly unrelated regression; Implied volatility;
    All these keywords.

    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

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