We derive closed form solutions to the discounted optimal stopping problems related to the pricing of the perpetual American standard put and call options in a diffusion model with piecewise-linear coefficients. The method of proof is based on the reduction of the initial optimal stopping...

Turbo warrant is a special type of barrier options in which the rebate is calculated as another exotic option. In this paper, using Laplace transforms we obtain the valuation of turbo warrants under mixed-exponential jump diffusion model, which is able to approximate any jump size distribution....

We obtain lower and upper bounds on option prices in one-dimensional jump-diffusion markets with point process components. Our proofs rely in general on the classical Kolmogorov equation argument and on the propagation of convexity property for Markov semigroups, but the bounds on intensities...

This paper studies the functional of the path of a diffusion in which volatility switches between two states: high and low. For this two-state Markov-chain model, we derive a closed-form expression for the distribution function for the time spent in the high volatility state by guessing the form...

In stochastic volatility models based on time-homogeneous diff usions, we provide a simple necessary and suffi cient condition for the discretely sampled fair strike of a variance swap to converge to the continuously sampled fair strike. It extends Theorem 3.8 of Jarrow, Kchia, Larsson and...