| Abstract: |
| In this talk we present a bridge representation for the finite dimensional joint density of stochastic process driven by Gaussian processes. A small time approximation of the joint density is readily obtained by approximate the bridge representation by a single deterministic path, which in the classical case recovers the heat kernel expansion for diffusion processes. Applications of such small time approximations include small time asymptotic for prices and implied volatilities of European or Asian equity options, options on realized variance, as well as an approximate maximum likelihood estimator. |
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