Robust Stochastic Discount Factors

  • Date: 01/25/2007

Tan Wang (University of British Columbia)


University of British Columbia


When market is incomplete a new non-redundant derivative security
cannot be priced by no arbitrage arguments alone. Moreover there will
be a multiplicity of stochastic discount factors and each of them may
give a different price for the new derivative security. This paper
develops an approach to the selection of a stochastic discount factor
for pricing a new derivative security. The approach is based on the
idea that the price of a derivative security should not vary too much
when the payoff of the primitive security is slightly perturbed, i.e.,
the price of the derivative should be robust to model misspecification.
The paper develops two metrics of robustness. The first is based on
robustness in expectation. The second is based on robustness in
probability and draws on tools from the theory of large deviations. We
show that in a stochastic volatility model, the two metrics yield
analytically tractable bounds for the derivative price as the
underlying stochastic volatility model is perturbed. The bounds can be
readily used for numerical examination of the sensitivity of the price
of the derivative to model misspecification.

Other Information: 

MITACS Math Finance Seminar 2007