Related papers: On a pricing problem for a multi-asset option with…
When the underlying asset displays oscillations, spikes or heavy-tailed distributions, the lognormal diffusion process (for which Black and Scholes developed their momentous option pricing formula) is inadequate: in order to overcome these…
This paper covers a massive acceleration of Monte-Carlo based pricing method for financial products and financial derivatives. The method is applicable in risk management settings, where a financial product has to be priced under a number…
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…
The space of call price functions has a natural noncommutative semigroup structure with an involution. A basic example is the Black--Scholes call price surface, from which an interesting inequality for Black--Scholes implied volatility is…
This study deals with the problem of pricing European currency options in discrete time setting, whose prices follow the fractional Black Scholes model with transaction costs. Both the pricing formula and the fractional partial differential…
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…
We consider conditional-mean hedging in a fractional Black-Scholes pricing model in the presence of proportional transaction costs. We develop an explicit formula for the conditional-mean hedging portfolio in terms of the recently…
The Black-Scholes option pricing model remains a cornerstone in financial mathematics, yet its application is often challenged by the need for accurate hedging strategies, especially in dynamic market environments. This paper presents a…
We consider fractional Black-Scholes market with proportional transaction costs. When transaction costs are present, one trades periodically i.e. we have the discrete trading with equidistance $n^{-1}$ between trading times. We derive a non…
We consider the computation of model-free bounds for multi-asset options in a setting that combines dependence uncertainty with additional information on the dependence structure. More specifically, we consider the setting where the…
This article considers the pricing and hedging of a call option when liquidity matters, that is, either for a large nominal or for an illiquid underlying asset. In practice, as opposed to the classical assumptions of a price-taking agent in…
Options are financial instruments that depend on the underlying stock. We explain their non-Gaussian fluctuations using the nonextensive thermodynamics parameter $q$. A generalized form of the Black-Scholes (B-S) partial differential…
American options are studied in a general discrete market in the presence of proportional transaction costs, modelled as bid-ask spreads. Pricing algorithms and constructions of hedging strategies, stopping times and martingale…
We provide representations of solutions to terminal value problems of inhomogeneous Black-Scholes equations and studied such general properties as min-max estimates, gradient estimates, monotonicity and convexity of the solutions with…
The change of numeraire gives very important computational simplification in option pricing. This technique reduces the number of sources of risks that need to be accounted for and so it is useful in pricing complicated derivatives that…
Refining a discrete model of Cheuk and Vorst we obtain a closed formula for the price of a European lookback option at any time between emission and maturity. We derive an asymptotic expansion of the price as the number of periods tends to…
In this paper we study both analytic and numerical solutions of option pricing equations using systems of orthogonal polynomials. Using a Galerkin-based method, we solve the parabolic partial diferential equation for the Black-Scholes model…
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…
The purpose of this paper is to construct the early exercise boundary for a class of nonlinear Black--Scholes equations with a nonlinear volatility depending on the option price. We review a method how to transform the problem into a…
A number of Bermudan option pricing methods that are applicable to options on multiple assets are studied in this thesis, one of the dominating questions being the natural scaling needed to extrapolate from Bermudan to American (both…