We consider a special family of occupation-time derivatives, namely proportional step options introduced by [18]. We develop new closed-form spectral expansions for pricing such options under a class of nonlinear volatility diffusion processes which includes the constant-elasticity-of-variance...

We introduce a mean-reverting SDE whose solution is naturally defined on the space of correlation matrices. This SDE can be seen as an extension of the well-known Wright–Fisher diffusion. We provide conditions that ensure weak and strong uniqueness of the SDE, and describe its ergodic limit....

We study the problem of parameter estimation for stochastic differential equations with small noise and fast oscillating parameters. Depending on how fast the intensity of the noise goes to zero relative to the homogenization parameter, we consider three different regimes. For each regime, we...

We give a new sufficient condition of the quasi-Gibbs property. This result is a refinement of one given in a previous paper (Osada (in press) [18]), and will be used in a forthcoming paper to prove the quasi-Gibbs property of Airy random point fields (RPFs) and other RPFs appearing under...

Summary We introduce a class of optimal stopping problems in which the gain is at least a fraction of the initial value. From a financial point of view this structure can be seen as a guarantee for the holder of an American option. It turns out that the optimal strategies are of two-sided type...

This article proposes an estimation procedure for the affine stochastic volatility models with jumps both in the asset price and variance processes. The estimation procedure is based on the joint (here bi-variate) unconditional characteristic function for the stochastic process for which we...

The paper develops a consumption based equilibrium model, focusing on the risk premium and the risk-free interest rate. We derive testable expressions for these quantities, and confront these with sample estimates for the 20. century. Our framework is a dynamic model in continuous time, allowing...