Path-Dependent Volatility

12 Pages Posted: 15 Apr 2014 Last revised: 11 Sep 2014

See all articles by Julien Guyon

Julien Guyon

Bloomberg L.P.; Columbia University - Department of Mathematics; New York University - Courant Institute of Mathematical Sciences

Date Written: September 10, 2014

Abstract

So far, path-dependent volatility models have drawn little attention from both practitioners and academics compared to local volatility and stochastic volatility models. This is unfair: in this article we show that they combine benefits from both. Like the local volatility model, they are complete and can fit exactly the market smile; like stochastic volatility models, they can produce rich implied volatility dynamics. Not only that: given their huge flexibility, they can actually generate a much broader range of spot-vol dynamics, thus possibly preventing large mispricings, and they can also capture prominent historical patterns of volatility. We give many examples to showcase their capabilities.

Keywords: Option pricing, path-dependent volatility, complete models, smile calibration, particle method, implied volatility dynamics, ARCH/GARCH models

JEL Classification: G13

Suggested Citation

Guyon, Julien, Path-Dependent Volatility (September 10, 2014). Available at SSRN: https://ssrn.com/abstract=2425048 or http://dx.doi.org/10.2139/ssrn.2425048

Julien Guyon (Contact Author)

Bloomberg L.P. ( email )

731 Lexington Avenue
New York, NY 10022
United States

Columbia University - Department of Mathematics ( email )

3022 Broadway
New York, NY 10027
United States

New York University - Courant Institute of Mathematical Sciences ( email )

New York University
New York, NY 10012
United States

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