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Stochastic Models of Implied Volatility Surfaces
Author(s) -
Cont Rama,
Fonseca Jose da,
Durrleman Valdo
Publication year - 2002
Publication title -
economic notes
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 0.274
H-Index - 19
eISSN - 1468-0300
pISSN - 0391-5026
DOI - 10.1111/1468-0300.00090
Subject(s) - implied volatility , volatility smile , volatility (finance) , econometrics , stochastic volatility , forward volatility , sabr volatility model , moneyness , volatility swap , economics , local volatility , valuation of options
We propose a market–based approach to the modelling of implied volatility, in which the implied volatility surface is directly used as the state variable to describe the joint evolution of market prices of options and their underlying asset. We model the evolution of an implied volatility surface by representing it as a randomly fluctuating surface driven by a finite number of orthogonal random factors. Our approach is based on a Karhunen–Loeve decomposition of the daily variations of implied volatilities obtained from market data on SP500 and DAX options. We illustrate how this approach extends and improves the accuracy of the well–known ‘sticky moneyness’ rule used by option traders for updating implied volatilities. Our approach gives a justification for the use of ‘Vegas’ for measuring volatility risk and provides a decomposition of volatility risk as a sum of independent contributions from empirically identifiable factors. (J.E.L.: G130, C14, C31).