EXPLICIT IMPLIED VOLATILITIES FOR MULTIFACTOR LOCAL‐STOCHASTIC VOLATILITY MODELS. (29th September 2015)

• Record Type: Journal Article
• Authors: Lorig, Matthew; Pagliarani, Stefano; Pascucci, Andrea
• Is Part Of: Mathematical finance. Volume 27:Number 3(2017:Jul.)
• Page Start: 926
• Page End: 960
• Publication Date: 2015-09-29
• Subjects: implied volatility -- local‐stochastic volatility -- CEV -- Heston -- SABR; Business mathematics -- Periodicals; 332
• DOI: 10.1111/mafi.12105
• Languages: English
• ISSNs: 0960-1627

Abstract

Abstract : We consider an asset whose risk‐neutral dynamics are described by a general class of local‐stochastic volatility models and derive a family of asymptotic expansions for European‐style option prices and implied volatilities. We also establish rigorous error estimates for these quantities. Our implied volatility expansions are explicit; they do not require any special functions nor do they require numerical integration. To illustrate the accuracy and versatility of our method, we implement it under four different model dynamics: constant elasticity of variance local volatility, Heston stochastic volatility, three‐halves stochastic volatility, and SABR local‐stochastic volatility.