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Stochastic Volatility Corrections to Black-Scholes
October 16, 2000
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Abstract:
We consider stochastic volatility models to account for the
smile or in other words the observed non-flat implied volatility
surface in European options. From data analysis we infer that the
volatility process is running on a faster scale than typical
maturities which leads to a singular perturbation of the Black-Scholes
equation. We identify the leading correction and show how to calibrate it
from derivative prices. It turns out that this correction is model
independent and stable in time. Applications to other exotic or American
derivatives are also given and hedging startegies are discussed.
This is a joint work with G. Papanicolaou (Stanford University) and R. Sircar (Princeton University). |
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2001 Purdue University Last Update: July 10, 2001 Please send comments and suggestions to the Webmaster. |