Related papers: Barrier Options under L\'evy Processes: a Simple S…
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…
In this paper we introduce a new approach to model-free path-dependent option pricing. We first introduce a general duality result for linear optimisation problems over signed measures introduced in [3] and show how the the problem of…
Financial markets based on L\'evy processes are typically incomplete and option prices depend on risk attitudes of individual agents. In this context, the notion of utility indifference price has gained popularity in the academic circles.…
In the quest for market mechanisms that are easy to implement, yet close to optimal, few seem as viable as posted pricing. Despite the growing body of impressive results, the performance of most posted price mechanisms however, rely…
For a one-dimensional L\'{e}vy process, we derive an explicit formula for the probability of first hitting a specified point among a fixed finite set. Moreover, using this formula, we obtain an explicit expression for each entry of the…
Options have provided a field of much study because of the complexity involved in pricing them. The Black-Scholes equations were developed to price options but they are only valid for European styled options. There is added complexity when…
An obvious way to simulate a L\'evy process $X$ is to sample its increments over time $1/n$, thus constructing an approximating random walk $X^{(n)}$. This paper considers the error of such approximation after the two-sided reflection map…
A time-dependent double-barrier option is a derivative security that delivers the terminal value $\phi(S_T)$ at expiry $T$ if neither of the continuous time-dependent barriers $b_\pm:[0,T]\to \RR_+$ have been hit during the time interval…
In this work, the Fourier-cosine series (COS) method has been combined with the Boundary Element Method (BEM) for a fast evaluation of barrier option prices. After a description of its use in the Black and Scholes (BS) model, the focus of…
We consider Markov decision processes where the state of the chain is only given at chosen observation times and of a cost. Optimal strategies involve the optimisation of observation times as well as the subsequent action values. We…
An efficient conditioning technique, the so-called Brownian Bridge simulation, has previously been applied to eliminate pricing bias that arises in applications of the standard discrete-time Monte Carlo method to evaluate options written on…
We consider the passage time problem for L\'evy processes, emphasising heavy tailed cases. Results are obtained under quite mild assumptions, namely, drift to $-\infty$ a.s. of the process, possibly at a linear rate (the finite mean case),…
The present article studies geometric step options in exponential L\'evy markets. Our contribution is manifold and extends several aspects of the geometric step option pricing literature. First, we provide symmetry and parity relations and…
This brief manuscript provides an introduction to L\'evy processes and their applications in finance as the random process that drives asset models. Characteristic functions and random variable generators of popular L\'evy processes are…
We give sufficient conditions on the rates of two asymmetric exclusion processes such that the existence of a blocking invariant measure for the first implies the existence of such a measure for the second. The main tool is a coupling…
In this article we propose a novel approach to reduce the computational complexity of various approximation methods for pricing discrete time American options. Given a sequence of continuation values estimates corresponding to different…
We study a stochastic control problem where the underlying process follows a spectrally negative L\'{e}vy process. A controller can continuously increase the process but only decrease it at independent Poisson arrival times. We show the…
In a model with no given probability measure, we consider asset pricing in the presence of frictions and other imperfections and characterize the property of coherent pricing, a notion related to (but much weaker than) the no arbitrage…
We derive explicit valuation formulae for an exotic path-dependent interest rate derivative, namely an option on the composition of LIBOR rates. The formulae are based on Fourier transform methods for option pricing. We consider two models…
Consider a one-sided Markov additive process with an upper and a lower barrier, where each can be either reflecting or terminating. For both defective and non-defective processes and all possible scenarios we identify the corresponding…