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Density expansions for hypoelliptic diffusions $(X^1,...,X^d)$ are revisited. In particular, we are interested in density expansions of the projection $(X_T^1,...,X_T^l)$, at time $T>0$, with $l leq d$. Global conditions are found which replace the well-known not-in-cutlocus condition known from heat-kernel asymptotics. Our small noise expansion allows for a second order exponential factor. As application, new light is shed on the Takanobu--Watanabe expansion of Brownian motion and Levys stochastic area. Further applications include tail and implied volatility asymptotics in some stochastic volatility models, discussed in a compagnion paper.
We extend the Bismut-Elworthy-Li formula to non-degenerate jump diffusions and payoff functions depending on the process at multiple future times. In the spirit of Fournie et al [13] and Davis and Johansson [9] this can improve Monte Carlo numerics f
We study the stochastic solution to a Cauchy problem for a degenerate parabolic equation arising from option pricing. When the diffusion coefficient of the underlying price process is locally Holder continuous with exponent $deltain (0, 1]$, the stoc
(Renegar, 2016) introduced a novel approach to transforming generic conic optimization problems into unconstrained, uniformly Lipschitz continuous minimization. We introduce radial transformations generalizing these ideas, equipped with an entirely n
Following Boukai (2021) we present the Generalized Gamma (GG) distribution as a possible RND for modeling European options prices under Hestons (1993) stochastic volatility (SV) model. This distribution is seen as especially useful in situations in w
This paper proposes the sample path generation method for the stochastic volatility version of CGMY process. We present the Monte-Carlo method for European and American option pricing with the sample path generation and calibrate model parameters to