Related papers: Classification of barrier options
In the present paper, we introduce a numerical scheme for the price of a barrier option when the price of the underlying follows a diffusion process. The numerical scheme is based on an extension of a static hedging formula of barrier…
State discrimination with the aim to minimize the error probability is a well studied problem. Instead, here the binary decision problem for operators with a given prior is investigated. A black box containing the unknown operator is probed…
Understanding how the optimal value of an optimisation problem changes when its input data is modified is an old question in mathematical optimisation. This paper investigates the computation of the optimal values of a family of (possibly…
Spread options are a fundamental class of derivative contract written on multiple assets, and are widely used in a range of financial markets. There is a long history of approximation methods for computing such products, but as yet there is…
In an observed generalized semi-Markov regime, estimation of transition rate of regime switching leads towards calculation of locally risk minimizing option price. Despite the uniform convergence of estimated step function of transition…
We show that prices and shortfall risks of game (Israeli) barrier options in a sequence of binomial approximations of the Black--Scholes (BS) market converge to the corresponding quantities for similar game barrier options in the BS market…
Finite difference approximations to multi-asset American put option price are considered. The assets are modelled as a multi-dimensional diffusion process with variable drift and volatility. Approximation error of order one quarter with…
We continue a series of papers devoted to construction of semi-analytic solutions for barrier options. These options are written on underlying following some simple one-factor diffusion model, but all the parameters of the model as well as…
In a market with transaction costs, the price of a derivative can be expressed in terms of (preconsistent) price systems (after Kusuoka (1995)). In this paper, we consider a market with binomial model for stock price and discuss how to…
This paper presents a general framework about what is a decision problem. Our motivation is related to the fact that decision analysis and operational research are structured (as disciplines) around classes of methods, while instead we…
A structure called a decision making problem is considered. The set of outcomes (consequences) is partially ordered according to the decision maker's preferences. The problem is how these preferences affect a decision maker to prefer one of…
With some transformations, we convert the problem of option pricing under state-dependent volatility into an initial value problem of the Fokker-Planck equation with a certain potential. By using the Lie symmetry analysis and similarity…
In this paper new analytical and numerical approaches to valuating path-dependent options of European type have been developed. The model of stochastic volatility as a basic model has been chosen. For European options we could improve the…
We examine optimal quadratic hedging of barrier options in a discretely sampled exponential L\'{e}vy model that has been realistically calibrated to reflect the leptokurtic nature of equity returns. Our main finding is that the impact of…
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…
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…
Firms that price perishable resources -- airline seats, hotel rooms, seasonal inventory -- now routinely use demand predictions, but these predictions vary widely in quality. Under hard capacity constraints, acting on an inaccurate…
The problem of stock hedging is reconsidered in this paper, where a put option is chosen from a set of available put options to hedge the market risk of a stock. A formula is proposed to determine the probability that the potential loss…
We consider as given a discrete time financial market with a risky asset and options written on that asset and determine both the sub- and super-hedging prices of an American option in the model independent framework of ArXiv:1305.6008. We…
Theoretical models applied to option pricing should take into account the empirical characteristics of the underlying financial time series. In this paper, we show how to price basket options when assets follow a shifted log-normal process…