From implied to spot volatilities |
| |
Authors: | Valdo Durrleman |
| |
Institution: | 1. Centre de Mathématiques Appliquées, école Polytechnique–CNRS, Route de Saclay, 91128, Palaiseau, France
|
| |
Abstract: | This paper is concerned with the relation between spot and implied volatilities. The main result is the derivation of a new
equation which gives the dynamics of the spot volatility in terms of the shape and the dynamics of the implied volatility
surface. This equation is a consequence of no-arbitrage constraints on the implied volatility surface right before expiry.
We first observe that the spot volatility can be recovered from the limit, as the expiry tends to zero, of at-the-money implied
volatilities. Then, we derive the semimartingale decomposition of implied volatilities at any expiry and strike from the no-arbitrage
condition. Finally the spot volatility dynamics is found by performing an asymptotic analysis of these dynamics as the expiry
tends to zero. As a consequence of this equation, we give general formulas to compute the shape of the implied volatility
surface around the at-the-money strike and for short expiries in general spot volatility models. |
| |
Keywords: | |
本文献已被 SpringerLink 等数据库收录! |
|