Asset Pricing under uncertainty

Details Asset Pricing under uncertainty Asset Pricing under uncertainty

2012-03-26

arxiv.org/abs/1203.5664v1

Economy

Quantitative Finance

Pricing of Securities

arXiv admin note: substantial text overlap with arXiv:1001.5202

Scientific paper

We study the effect of parameter uncertainty on a stochastic diffusion model, in particular the impact on the pricing of contingent claims, using methods from the theory of Dirichlet forms. We apply these techniques to hedging procedures in order to compute the sensitivity of SDE trajectories with respect to parameter perturbations. We show that this analysis can justify endogenously the presence of a bid-ask spread on the option prices. We also prove that if the stochastic differential equation admits a closed form representation then the sensitivities have closed form representations. We examine the case of log-normal diffusion and we show that this framework leads to a smiled implied volatility surface coherent with historical data.

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