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

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.

On the implied market price of risk under the stochastic numéraire

“…To simplify notation, we will describe it as the following: we assume that the processes a(t), Further, let us consider the problem of estimation of ER 2 θ for the discounted hedging error R θ . This error is represented in (11)- (14) as…”