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An approximation formula for normal implied volatility under general local stochastic volatility models
Author(s) -
Karami Yasaman,
Shiraya Kenichiro
Publication year - 2018
Publication title -
journal of futures markets
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 0.88
H-Index - 55
eISSN - 1096-9934
pISSN - 0270-7314
DOI - 10.1002/fut.21931
Subject(s) - stochastic volatility , local volatility , implied volatility , volatility (finance) , econometrics , sabr volatility model , monte carlo method , heston model , volatility smile , mathematics , economics , statistical physics , statistics , physics
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.