Calibration of Stock Betas from Skews of Implied Volatilities

Start: 04/09/2009 - 4:15pm
End  : 04/09/2009 - 5:15pm

Statistics/OR/Math Finance Seminar

Jean-Pierre Fouque (UCSB)


We develop call option price approximations for both the market index and
an individual asset using a singular perturbation of a continuous time
Capital Asset Pricing Model (CAPM) in a stochastic volatility environment.
These approximations show the role played by the asset's beta parameter as
a component of the parameters of the call option price of the asset. They
also show how these parameters, in combination with the parameters of the
call option price for the market, can be used to extract the beta
parameter. Finally, a calibration technique for the beta parameter is
derived using the estimated option price parameters of both the asset and
market index. The resulting estimator of the beta parameter is not only
simple to implement but has the advantage of being forward-looking as it
is calibrated from skews of implied volatilities.

Joint work with Eli Kollman (UCSB)

Beckman Auditorium (Beckman B126) Thursday April 9 4:15-5:15pm