
Financial Mathematics Seminars  January 30, 2002
Abstracts
Dynamic Mixture Models of Option
Pricing
Eric Renault, Université de Montréal 

The valuation of security prices and
sensitivities lends to the evaluation of expectations with respect
to the probability distribution of a number of state variables.
Like for conditional MonteCarlo, conditioning on some state variables
is a fruitful technique if it allows to do part of the integration
analytically. Option prices and sensitivities then appear as mixtures
of popular closedfrom formulas. This paper makes this approach
systematic in the context of arbitrage pricing. It characterizes
the specific distributional features of the joint stochastic process
of state variables and assets dividends which make possible riskneutral
valuation as typically attributed to complete markets. In this case,
option pricing formulas do not explicitly depend upon the risk premium
for the underlying asset. Besides, the paper stresses how some instantaneous
correlation between asset returns and mixing state variables precludes
preferencefree option pricing. This effect is also characterized
in terms of volatility smile skewness and shown to be empirically
relevant for S&P 500 call option pricing.

Preferences, State Variables and Option Pricing
René Garcia, Université de Montréal 

This paper assesses the empirical performance of an intertemporal
option pricing model with latent variables which generalizes the
BlackScholes and the stochastic volatility formulas. We derive
a closedform formula for an equilibrium model with recursive
preferences where the fundamentals follow a Markov switching process.
In a simulation experiment based on the model, we show that option
prices are more informative about preference parameters than stock
returns. When we estimate the preference parameters implicit in
S&P 500 call option prices given our model, we find quite
reasonable values for the coefficient of relative risk aversion
and the intertemporal elasticity of substitution. Finally, when
we calibrate the model to minimize outofsample pricing errors,
we are in the same order of magnitude as the ad hoc BS model of
Dumas, Fleming and Whaley (1998).


