Title: On the implied volatility layers under the future risk-free rate uncertainty

Authors: Lin-Yee Hin; Nikolai Dokuchaev

Addresses: Department of Mathematics and Statistics, Curtin University, GPO Box U1987, Perth, 6845, Western Australia ' Department of Mathematics and Statistics, Curtin University, GPO Box U1987, Perth, 6845, Western Australia

Abstract: This paper suggests a method of estimation of the implied volatility smile uncertainty of the observed options prices due to future risk-free rate uncertainty. The purpose is to quantify the range of uncertainty under different scenarios. We consider the setting where both the implied volatility and the risk free rate are calculated jointly from the observed option prices. Due to the cumulative risk-free rate uncertainty, the corresponding system of equations is underdetermined, leading to uncertainty in the volatility surface. We estimate the size of implied volatility layers between the surfaces representing the upper and lower bounds for the implied volatilities for the future risk-free rate uncertainty, defined by current Libor rate and the size of fluctuation estimated from the historical data.

Keywords: implied volatility surfaces; IVSs; implied volatility layers; risk-free rate term structure; interest rate forecasting; rate uncertainty; options pricing; Libor rate; fluctuation size.

DOI: 10.1504/IJFMD.2014.062395

International Journal of Financial Markets and Derivatives, 2014 Vol.3 No.4, pp.392 - 408

Received: 28 Oct 2013
Accepted: 07 Apr 2014
Published online: 30 Jun 2014 *

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