## 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.

MITACS Math Finance Seminar 2007