Local-Stochastic Volatility for Vanilla Modeling: A Tractable and Arbitrage Free Approach to Option Pricing

Autor: Dominique R. A. Bang
Rok vydání: 2018
Předmět:
Zdroj: SSRN Electronic Journal.
ISSN: 1556-5068
DOI: 10.2139/ssrn.3171877
Popis: We present a novel and flexible technique for the construction of tractable, and fully arbitrage-free, Local-Stochastic Volatility (LSV) term distribution models. The method utilizes Lamperti’s harmonic transform to combine a pure stochastic volatility (SV) process MT with a general local volatility (LV) function σ. European options prices can conveniently be expressed in terms of a 1-dimensional integral over options on the SV component MT. As a demonstration, we apply the technique to the popular SABR model family by letting MT be the Normal SABR process, and letting the LV function σ be an extended CEV function, endowed with additional controls over the backbone and the wings for the smile. The resulting model not only rectifies the arbitrage problems of commonly used expansions for the SABR class, its additional parameters also allow for adequate handling of non-positive rates and improved calibration to quoted swaptions and CMS forward rates. Finally, for variety we also illustrate the technique using Heston dynamics and a general piece-wise linear LV function.
Databáze: OpenAIRE
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