A theory of non-Gaussian option pricing: capturing the smile and the skew
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Date: 10-20-2003
Start Time:
5:30pm
End Time: 7:00pm
Speaker: Lisa Borland, Evnine-Vaughan Associates Inc.
Location: Hamilton 717
ABSTRACT
We introduce a new model of stock returns that results in fat-tailed (power-law)
Student distributions rather than Gaussians. These distributions are
characterized by an index q, related to the Tsallis generalized entropy that we
use to model the evolution of fluctuations. For q =1 the standard Black-Scholes
case is recovered. Based on this model, which is a statistical feedback process
for returns, one finds a martingale representation and simple closed form
pricing equations for European calls. Most empirical distributions of returns
are well-fitted with q around 1.5. Using that value of q in the option pricing
formulas yields results which match empirically observed prices and volatility
smiles very well (for example for options on currency futures), using just one
value of sigma across all strikes. In a simple manner, we also show how this
model can be extended to account for skew.