Functional Ito Calculus and Robust Volatility Hedge
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Date: 01-29-2009
Start Time:
5:30pm
End Time: 7:00pm
Speaker: Bruno Dupire, Bloomberg LP
Location: Park Avenue Plaza at 55 East 52nd Street
ABSTRACT
We present an extension of Ito calculus to functionals of price paths. When applied in a diffusion framework to the expectation of a path dependent claim conditional on the path so far, it leads to a Black-Scholes like PDE for path dependent options, even if the path dependency cannot be summarized by a finite number of state variables, with the classical Gamma/Theta (properly defined) trade-off. It also gives an alternative expression of the Clark-Ocone formula for the Martingale Representation Theorem.
We apply the functional Ito Formula to obtain the difference of price of an exotic option in two different models and deduce the sensitivity of the price to local deformations of the implied volatility surface. It leads to a decomposition of the Vega across strikes and maturities and the associated hedge in terms of a portfolio of European options.
BIO
After having headed derivatives research teams at Société Générale, Paribas and Nikko FP where he was a Managing Director, Bruno joined Bloomberg L.P. in 2004. He is best known for his work on volatility modelling, including the Local Volatility Model (1993), simplest extension of the Black-Merton-Scholes model to fit all option prices, and subsequent results on stochastic volatility and volatility derivatives. His current interests include quantitative trading strategies and robust hedging.
He was included in December 2002 in the Risk magazine "Hall of Fame" of the 50 most influential people in the history of derivatives. He is the recipient of the 2006 "Cutting edge research" Wilmott award and has been voted in 2006 the most important derivatives practitioner of the previous 5 years in the ICBI Global Derivatives industry survey. Bruno is the recipient of the Risk Magazine 2008 "Life Achievement Award".
*There will be a cocktail following the event.
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