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Long-Term Behaviors and Implied Volatilities in General Affine Diffusion Models
Long-Term Behaviors Implied Volatilities General Affine Diffusion Models
2010/10/22
This paper considers asset price dynamics of which discounted return is modeled by a multi-dimensional affine diffusion process. By analyzing the Riccati system, which is associated with the affine p...
Semi-Closed Form Cubature and Applications to Financial Diffusion Models
Semi-Closed Cubature Applications Financial Diffusion Models
2010/10/21
Cubature methods, a powerful alternative to Monte Carlo due to Kusuoka~[Adv.~Math.~Econ.~6, 69--83, 2004] and Lyons--Victoir~[Proc.~R.~Soc.\\Lond.~Ser.~A 460, 169--198, 2004], involve the solution to...
Two-sided estimates for stock price distribution densities in jump-diffusion models
Stochastic volatility models Jump-diffusion models Stock
2010/10/20
We consider uncorrelated Stein-Stein, Heston, and Hull-White models and their perturbations by compound Poisson processes with jump amplitudes distributed according to a double exponential law. Simila...
Deterministic criteria for the absence of arbitrage in one-dimensional diffusion models
Deterministic criteria arbitrage one-dimensional diffusion models
2010/10/20
We obtain a deterministic characterisation of the \emph{no free lunch with vanishing risk}, the \emph{no generalised arbitrage} and the \emph{no relative arbitrage} conditions in the one-dimensional d...
On a class of semi-elliptic diffusion models. Part I: a constructive analytical approach for global existence, densities, and numerical schemes
Degenerate parabolic equations financial derivatives
2010/10/18
Semi-elliptic stochastic differential equations (SDEs) are common models among practitioners. However, value functions and sensitivities of such models are described by degenerate parabolic partial d...
Using pseudo-parabolic and fractional equations for option pricing in jump diffusion models
option pricing jump diffusion models
2010/10/18
In mathematical finance a popular approach for pricing options under some Levy model is to consider underlying that follows a Poisson jump diffusion process. As it is well known this results in a par...
Solvable Nonlinear Volatility Diffusion Models with Affine Drift
Solvable Nonlinear Volatility Diffusion Models Affine Drift
2010/11/1
We present a method for constructing new families of solvable one-dimensional di usions with linear drift and nonlinear di usion coecient functions, whose tran-sition densities are obtainable in anal...
Generalized pricing formulas for stochastic volatility jump diffusion models applied to the exponential Vasicek model
pricing formulas diffusion models the exponential Vasicek model
2010/12/13
Path integral techniques for the pricing of financial options are mostly based on models that can be recast in terms of a Fokker-Planck differential equation and that, consequently, neglect jumps and...