Related papers: Digital double barrier options: Several barrier pe…
We study a method of reducing space dimension in multi-dimensional Black-Scholes partial differential equations as well as in multi-dimensional parabolic equations. We prove that a multiplicative transformation of space variables in the…
A master equation approach to the numerical solution of option pricing models is developed. The basic idea of the approach is to consider the Black--Scholes equation as the macroscopic equation of an underlying mesoscopic stochastic option…
The pricing and hedging of a general class of options (including American, Bermudan and European options) on multiple assets are studied in the context of currency markets where trading is subject to proportional transaction costs, and…
We study the pricing and hedging of European spread options on correlated assets when, in contrast to the standard framework and consistent with imperfect liquidity markets, the trading in the stock market has a direct impact on stocks…
In this paper we analyze a nonlinear Black--Scholes model for option pricing under variable transaction costs. The diffusion coefficient of the nonlinear parabolic equation for the price $V$ is assumed to be a function of the underlying…
The aim of this paper is to study the continuity correction for barrier options in jump-diusion models. For this purpose, we express the pay-off a barrier option in terms of the maximum of the underlying process. We then condition with…
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…
Options are contingent claims regarding the value of underlying assets. The Black-Scholes formula provides a road map for pricing these options in a risk-neutral setting, justified by a delta hedging argument in which countervailing…
Accurate prediction of electricity prices plays an essential role in the electricity market. To reflect the uncertainty of electricity prices, price intervals are predicted. This paper proposes a novel prediction interval construction…
Two novel closed-form formulas for the price of barrier options in stochastic volatility models with zero interest rate and dividend yield but nonzero correlation between the asset and its instantaneous volatility are derived. The first is…
Double no-touch options, contracts which pay out a fixed amount provided an underlying asset remains within a given interval, are commonly traded, particularly in FX markets. In this work, we establish model-free bounds on the price of…
We compare the option pricing formulas of Louis Bachelier and Black-Merton-Scholes and observe -- theoretically as well as for Bachelier's original data -- that the prices coincide very well. We illustrate Louis Bachelier's efforts to…
We consider the supervised learning problem of learning the price of an option or the implied volatility given appropriate input data (model parameters) and corresponding output data (option prices or implied volatilities). The majority of…
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…
In this paper we analyse financial implications of exchangeability and similar properties of finite dimensional random vectors. We show how these properties are reflected in prices of some basket options in view of the well-known put-call…
In this paper, we study a pricing problem of the multiple reset put option, which allows the holder to reset several times a current strike price to obtain an at-the-money European put option. We formulate the pricing problem as a multiple…
We introduce a new method of delta hedging. In many cases, this method results in a lower cost than the Black-Scholes method. To calculate the cost of hedging, we develop a Mathematica program that include the two-dimensional Newton-Raphson…
We present two models for incorporating the total effect of market microstructure noise into dynamic pricing of assets and European options. The first model is developed under a Black-Scholes-Merton, continuous-time framework. The second…
Accurate option pricing is essential for effective trading and risk management in financial markets, yet it remains challenging due to market volatility and the limitations of traditional models like Black-Scholes. In this paper, we…
Option pricing is a significant problem for option risk management and trading. In this article, we utilize a framework to present financial data from different sources. The data is processed and represented in a form of 2D tensors in three…