Black-Scholes in a CEV Random Environment: A New Approach to Smile Modelling

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Title: Black-Scholes in a CEV Random Environment: A New Approach to Smile Modelling
Authors: Jacquier, A
Roome, P
Item Type: Journal Article
Abstract: Classical (Ito diffusions) stochastic volatility models are not able to capture the steepness of small-maturity implied volatility smiles. Jumps, in particular exponential Levy and affine models, which exhibit small-maturity exploding smiles, have historically been proposed to remedy this (see Tankov for an overview). A recent breakthrough was made by Gatheral, Jaisson and Rosenbaum, who proposed to replace the Brownian driver of the instantaneous volatility by a short-memory fractional Brownian motion, which is able to capture the short-maturity steepness while preserving path continuity. We suggest here a different route, randomising the Black-Scholes variance by a CEV-generated distribution, which allows us to modulate the rate of explosion (through the CEV exponent) of the implied volatility for small maturities. The range of rates includes behaviours similar to exponential Levy models and fractional stochastic volatility models. As a by-product, we make a conjecture on the small-maturity forward smile asymptotics of stochastic volatility models, in exact agreement with the results in Jacquier and Roome for the Heston model.
Issue Date: 27-Mar-2015
Date of Acceptance: 27-Mar-2015
Publisher: SSRN
Journal / Book Title: SSRN Electronic Journal
Copyright Statement: © The Authors
Sponsor/Funder: Engineering & Physical Science Research Council (EPSRC)
Funder's Grant Number: EP/M008436/1
Publication Status: Published
Appears in Collections:Financial Mathematics
Faculty of Natural Sciences

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