Related papers: On perpetual American put valuation and first-pass…
We consider the problem of valuation of American options written on dividend-paying assets whose price dynamics follows a multidimensional exponential Levy model. We carefully examine the relation between the option prices, related partial…
This paper presents a derivation of the explicit price for the perpetual American put option time-capped by the first drawdown epoch beyond a predefined level. We consider the market in which an asset price is described by geometric L\'evy…
In this paper, we will discuss an approximation of the characteristic function of the first passage time for a Levy process using the martingale approach. The characteristic function of the first passage time of the tempered stable process…
This paper presents the solution to a European option pricing problem by considering a regime-switching jump diffusion model of the underlying financial asset price dynamics. The regimes are assumed to be the results of an observed pure…
We study the regularity of the stochastic representation of the solution of a class of initial-boundary value problems related to a regime-switching diffusion. This representation is related to the value function of a finite-horizon optimal…
Perpetual American options are financial instruments that can be readily exercised and do not mature. In this paper we study in detail the problem of pricing this kind of derivatives, for the most popular flavour, within a framework in…
In this paper we consider a jump-diffusion dynamic whose parameters are driven by a continuous time and stationary Markov Chain on a finite state space as a model for the underlying of European contingent claims. For this class of processes…
In this paper, we study a version of the perpetual American call/put option where exercise opportunities arrive only periodically. Focusing on the exponential L\'evy models with i.i.d. exponentially-distributed exercise intervals, we show…
We prove that the perpetual American put option price of level dependent volatility model with compound Poisson jumps is convex and is the classical solution of its associated quasi-variational inequality, that it is $C^2$ except at the…
We introduce an algorithm for the pricing of finite expiry American options driven by L\'evy processes. The idea is to tweak Carr's `Canadisation' method, cf. Carr [9] (see also Bouchard et al [5]), in such a way that the adjusted algorithm…
This paper considers the class of L\'evy processes that can be written as a Brownian motion time changed by an independent L\'evy subordinator. Examples in this class include the variance gamma model, the normal inverse Gaussian model, and…
The main objective of this paper is to present an algorithm of pricing perpetual American put options with asset-dependent discounting. The value function of such an instrument can be described as \begin{equation*}…
The Wiener-Hopf factorization is obtained in closed form for a phase type approximation to the CGMY L\'{e}vy process. This allows, for the approximation, exact computation of first passage times to barrier levels via Laplace transform…
This paper studies the valuation of a class of default swaps with the embedded option to switch to a different premium and notional principal anytime prior to a credit event. These are early exercisable contracts that give the protection…
We consider the problem of valuing a European option written on an asset whose dynamics are described by an exponential L\'evy-type model. In our framework, both the volatility and jump-intensity are allowed to vary stochastically in time…
We derive the explicit price of the perpetual American put option cancelled at the last passage time of the underlying above some fixed level. We assume the asset process is governed by a geometric spectrally negative L\'evy process. We…
In the present paper we present a finite element approach for option pricing in the framework of a well-known stochastic volatility model with jumps, the Bates model. In this model the asset log-returns are assumed to follow a…
In this paper we consider the following optimal stopping problem $$V^{\omega}_{\rm A}(s) = \sup_{\tau\in\mathcal{T}} \mathbb{E}_{s}[e^{-\int_0^\tau \omega(S_w) dw} g(S_\tau)],$$ where the process $S_t$ is a jump-diffusion process,…
We consider the problem of pricing American Exchange options driven by a L\'evy process. We study the properties of American Exchange options, we represented it as the sum of the price of the corresponding European exchange option price and…
Pricing financial or real options with arbitrary payoffs in regime-switching models is an important problem in finance. Mathematically, it is to solve, under certain standard assumptions, a general form of optimal stopping problems in…