Related papers: Binomial Approximations for Barrier Options of Isr…
We show that the shortfall risk of binomial approximations of game (Israeli) options converges to the shortfall risk in the corresponding Black--Scholes market considering Lipschitz continuous path-dependent payoffs for both discrete- and…
We justify and give error estimates for binomial approximations of game (Israeli) options in the Black--Scholes market with Lipschitz continuous path dependent payoffs which are new also for usual American style options. We show also that…
We show that shortfall risks of American options in a sequence of multinomial approximations of the multidimensional Black--Scholes (BS) market converge to the corresponding quantities for similar American options in the multidimensional BS…
We study shortfall risk minimization for American options with path dependent payoffs under proportional transaction costs in the Black--Scholes (BS) model. We show that for this case the shortfall risk is a limit of similar terms in an…
We study partial hedging for game options in markets with transaction costs bounded from below. More precisely, we assume that the investor's transaction costs for each trade are the maximum between proportional transaction costs and a…
In this paper we use Bernstein and Chebyshev polynomials to approximate the price of some basket options under a bivariate Black-Scholes model. The method consists in expanding the price of a univariate related contract after conditioning…
We derive error estimates for multinomial approximations of American options in a multidimensional jump--diffusion Merton's model. We assume that the payoffs are Markovian and satisfy Lipschitz type conditions. Error estimates for such type…
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…
Game (Israeli) options in a multi-asset market model with proportional transaction costs are studied in the case when the buyer is allowed to exercise the option and the seller has the right to cancel the option gradually at a mixed (or…
Expanding the ideas of the author's paper 'Nonexpansive maps and option pricing theory' (Kibernetica 34:6 (1998), 713-724) we develop a pure game-theoretic approach to option pricing, by-passing stochastic modeling. Risk neutral…
In this paper we propose a closed-form approximation for the price of basket options under a multivariate Black-Scholes model, based on Taylor expansions and the calculation of mixed exponential-power moments of a Gaussian distribution. Our…
This work addresses the problem of pricing American basket options in a multivariate setting, which includes among others, the Bachelier and the Black-Scholes models. In high dimensions, nonlinear partial differential equation methods for…
The pricing, hedging, optimal exercise and optimal cancellation of game or Israeli options are considered in a multi-currency model with proportional transaction costs. Efficient constructions for optimal hedging, cancellation and exercise…
We consider the problem of approximation of density functions which is important in the theory of pricing of basket options. Our method is well adopted to the multidimensional case. Observe that implementations of polynomial and spline…
Contrary to the common view that exact pricing is prohibitive owing to the curse of dimensionality, this study proposes an efficient and unified method for pricing options under multivariate Black-Scholes-Merton (BSM) models, such as the…
We give an exposition and numerical studies of upper hedging prices in multinomial models from the viewpoint of linear programming and the game-theoretic probability of Shafer and Vovk. We also show that, as the number of rounds goes to…
In this paper we study the existence of an optimal hedging strategy for the shortfall risk measure in the game options setup. We consider the continuous time Black--Scholes (BS) model. Our first result says that in the case where the game…
The present article provides an efficient and accurate hybrid method to price American standard options in certain jump-diffusion models as well as American barrier-type options under the Black & Scholes framework. Our method generalizes…
Suppose one buys two very similar stocks and is curious about how much, after some time T, one of them will contribute to the overall asset, expecting, of course, that it should be around 1/2 of the sum. Here we examine this question within…
We determine the price of digital double barrier options with an arbitrary number of barrier periods in the Black-Scholes model. This means that the barriers are active during some time intervals, but are switched off in between. As an…