Probabilistic Interpretation of an Implied Volatility Smile
Abstract
When the variance rates implied from option prices diﬀer across strike prices, at most one of them can be interpreted as the variance rate of the underlying security price. We develop an arbitragefree option pricing model... [ view full abstract ]
When the variance rates implied from option prices diﬀer across strike prices, at most one of them can be interpreted as the variance rate of the underlying security price. We develop an arbitragefree option pricing model with four stochastic state variables, one of which is the underlying security price. We show how to successively explicitly determine the other three state variables from three given coterminal arbitragefree implied variance rates. The resulting calibrated implied variance rate smile is given a simple probabilistic representation. To our knowledge, this is the ﬁrst nonﬂat implied variance rate smile enjoying any probabilistic interpretation.
Authors

Peter Carr
(New York University)

Liuren Wu
(Baruch College, CUNY)
Topic Areas
Options , Stochastic Volatility
Session
FRABU » Variance, Implied Volatility and Pricing (10:00  Friday, 20th July, Burke Theater)
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