An approximation formula for normal implied volatility under general local stochastic volatility models

Abstract

We approximate normal implied volatilities by means of an asymptotic expansion method. The contribution of this paper is twofold: to our knowledge, this paper is the first to provide a unified approximation method for the normal implied volatility under general local stochastic volatility models. Second, we applied our framework to polynomial local stochastic volatility models with various degrees and could replicate the swaptions market data accurately. In addition we examined the accuracy of the results by comparison with the Monte‐Carlo simulations.

A Black–Scholes user's guide to the Bachelier model

“…Perederiy (2018) extends the Vanna-Volga method (Castagna and Mercurio, 2007) from the original BS volatility context to the Bachelier model, which is helpful for the arbitrage-free interpolation of the volatility smile. Finally, while not strictly speaking an SV model, Karami and Shiraya (2018) provide an asymptotic expansion method to obtain the equivalent Bachelier volatility of the general local volatility models.…”