Related papers: Asian options and meromorphic Levy processes

In this paper, we study the asymptotic behavior of Asian option prices in the worst case scenario under an uncertain volatility model. We give a procedure to approximate the Asian option prices with a small volatility interval. By imposing…

This paper studies a class of optimal multiple stopping problems driven by L\'evy processes. Our model allows for a negative effective discount rate, which arises in a number of financial applications, including stock loans and real…

Within a path integral formalism for non-Gaussian price fluctuations we set up a simple stochastic calculus and derive a natural martingale for option pricing from the wealth balance of options, stocks, and bonds. The resulting formula is…

The challenge to fruitfully merge state-of-the-art techniques from mathematical finance and numerical analysis has inspired researchers to develop fast deterministic option pricing methods. As a result, highly efficient algorithms to…

In this paper we introduce an additive two-factor model for electricity futures prices based on Normal Inverse Gaussian L\'evy processes, that fulfills a no-overlapping-arbitrage (NOA) condition. We compute European option prices by Fourier…

We investigate the pricing of cliquet options in a geometric Meixner model. The considered option is of monthly sum cap style while the underlying stock price model is driven by a pure-jump Meixner--L\'{e}vy process yielding Meixner…

We develop at-the-money call-price and implied volatility asymptotic expansions in time to maturity for a class of asset-price models whose log returns follow a L\'evy process. Under mild assumptions placing the driving L\'evy process in…

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 partial integro-differential equation (PIDE)…

We derive a closed-form solution for the price of an average price as well as an average strike geometric Asian option, by making use of the path integral formulation. Our results are compared to a numerical Monte Carlo simulation. We also…

Semi-analytical pricing of American options in a time-dependent Ornstein-Uhlenbeck model was presented in [Carr, Itkin, 2020]. It was shown that to obtain these prices one needs to solve (numerically) a nonlinear Volterra integral equation…

An explicit martingale representation for random variables described as a functional of a Levy process will be given. The Clark-Ocone theorem shows that integrands appeared in a martingale representation are given by conditional…

Let $\{D(s), s \geq 0\}$ be a non-decreasing L\'evy process. The first-hitting time process $\{E(t) t \geq 0\}$ (which is sometimes referred to as an inverse subordinator) defined by $E(t) = \inf \{s: D(s) > t \}$ is a process which has…

For a converging sequence of exponential L\'evy models, we give conditions under which the associated sequence of option prices converges. We also study the behaviour of the prices when no such convergence holds. We then consider two…

We present an approximation method based on the mixing formula (Hull & White 1987, Romano & Touzi 1997) for pricing European options in Barndorff-Nielsen and Shephard models. This approximation is based on a Taylor expansion of the option…

We derive a small-time expansion for out-of-the-money call options under an exponential Levy model, using the small-time expansion for the distribution function given in Figueroa-Lopez & Houdre (2009), combined with a change of num\'eraire…

In the first part of this thesis, we focus on American options in the Heston model. We first give an analytical characterization of the value function of an American option as the unique solution of the associated (degenerate) parabolic…

For a L\'evy process $\xi=(\xi_t)_{t\geq0}$ drifting to $-\infty$, we define the so-called exponential functional as follows \[{\rm{I}}_{\xi}=\int_0^{\infty}e^{\xi_t} dt.\] Under mild conditions on $\xi$, we show that the following…

Using tools from spectral analysis, singular and regular perturbation theory, we develop a systematic method for analytically computing the approximate price of a derivative-asset. The payoff of the derivative-asset may be path-dependent.…

It is well known that the Black-Scholes-Merton model suffers from several deficiencies. Jump-diffusion and Levy models have been widely used to partially alleviate some of the biases inherent in this classical model. Unfortunately, the…

We consider a refracted jump diffusion process having two-sided jumps with rational Laplace transforms. For such a process, by applying a straightforward but interesting approach, we derive formulas for the Laplace transform of its…