Robust Stochastic Discount Factors
市场不完全时，新衍生品无法仅靠无套利定价，本文提出基于稳健性选择随机贴现因子的方法，开发了期望稳健性和概率稳健性两种度量，并在随机波动率模型中得到可解析处理的定价边界。
When the 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. The Author 2007. Published by Oxford University Press on behalf of The Society for Financial Studies. All rights reserved. For Permissions, please email: journals.permissions@oxfordjournals.org, Oxford University Press.