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

Yasaman Karami and Kenichiro Shiraya

Journal of Futures Markets, 2018, vol. 38, issue 9, 1043-1061

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.

Date: 2018
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