Related papers: Barrier Options under L\'evy Processes: a Simple S…
We use Lie symmetry methods to price certain types of barrier options. Usually Lie symmetry methods cannot be used to solve the Black-Scholes equation for options because the function defining the maturity condition for an option is not…
For a given level of accuracy in option prices, the paper considers the problem of deciding when exactly, as one or more of the pricing parameters change, a barrier option degenerates into a simpler type of option. This problem is…
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…
In this paper we present an algorithm for pricing barrier options in one-dimensional Markov models. The approach rests on the construction of an approximating continuous-time Markov chain that closely follows the dynamics of the given…
Pricing of high-dimensional options is a deep problem of the Theoretical Financial Mathematics. In this article we present a new class of L\'{e}vy driven models of stock markets. In our opinion, any market model should be based on a…
This paper deals with a high-order accurate implicit finite-difference approach to the pricing of barrier options. In this way various types of barrier options are priced, including barrier options paying rebates, and options on…
We provide analytical tools for pricing power options with exotic features (capped or log payoffs, gap options ...) in the framework of exponential L\'evy models driven by one-sided stable or tempered stable processes. Pricing formulas take…
We present the method of moments approach to pricing barrier-type options when the underlying is modelled by a general class of jump diffusions. By general principles the option prices are linked to certain infinite dimensional linear…
Exponential L\'evy processes have been used for modelling financial derivatives because of their ability to exhibit many empirical features of markets. Using their multidimensional analogue, a general analytic pricing formula is obtained,…
This paper sets out to provide a general framework for the pricing of average-type options via lower and upper bounds. This class of options includes Asian, basket and options on the volume-weighted average price. We demonstrate that in…
In this paper we propose a transform method to compute the prices and greeks of barrier options driven by a class of Levy processes. We derive analytical expressions for the Laplace transforms in time of the prices and sensitivities of…
Given a spectrally negative L\'evy process and independent Poisson observation times, we consider a periodic barrier strategy that pushes the process down to a certain level whenever it is above it. We also consider the versions with…
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…
We provided an analytical representation of the price of a barrier option with one type of special moving barrier. We consider the case that risk free rate, dividend rate and stock volatility are time dependent. We get a pricing formula and…
Barrier options are one of the most widely traded exotic options on stock exchanges. In this paper, we develop a new stochastic simulation method for pricing barrier options and estimating the corresponding execution probabilities. We show…
A statistical decision problem is hidden in the core of option pricing. A simple form for the price C of a European call option is obtained via the minimum Bayes risk, R_B, of a 2-parameter estimation problem, thus justifying calling C…
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…
In the paper, we develop a very fast and accurate method for pricing double barrier options with continuous monitoring in wide classes of L\'evy models; the calculations are in the dual space, and the Wiener-Hopf factorization is used. For…
Recent developments on financial markets have revealed the limits of Brownian motion pricing models when they are applied to actual markets. L\'evy processes, that admit jumps over time, have been found more useful for applications. Thus,…
We study valuation of swing options on commodity markets when the commodity prices are driven by multiple factors. The factors are modeled as diffusion processes driven by a multidimensional L\'evy process. We set up a valuation model in…