Related papers: Pricing American Call Options by the Black-Scholes…
We invert the Black-Scholes formula. We consider the cases low strike, large strike, short maturity and large maturity. We give explicitly the first 5 terms of the expansions. A method to compute all the terms by induction is also given. At…
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…
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 take the holistic approach of computing an OTC claim value that incorporates credit and funding liquidity risks and their interplays, instead of forcing individual price adjustments: CVA, DVA, FVA, KVA. The resulting nonlinear…
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 apply path integration techniques to obtain option pricing with stochastic volatility using a generalized Black-Scholes equation known as the Merton and Garman equation. We numerically simulate the option prices using the technique of…
We consider the problem of pricing basket options in a multivariate Black Scholes or Variance Gamma model. From a numerical point of view, pricing such options corresponds to moderate and high dimensional numerical integration problems with…
In this work, we present a quantum algorithm designed to solve the differential equation used in the pricing of Asian options, in the framework of the Black-Scholes model. Our approach modifies an existing quantum pre-conditioning method…
We extend the viscosity solution characterization proved in [5] for call/put American option prices to the case of a general payoff function in a multi-dimensional setting: the price satisfies a semilinear re-action/diffusion type equation.…
The purpose of this paper is to analyze the problem of option pricing when the short rate follows subdiffusive fractional Merton model. We incorporate the stochastic nature of the short rate in our option valuation model and derive explicit…
We present an adaptive approach for valuing the European call option on assets with stochastic volatility. The essential feature of the method is a reduction of uncertainty in latent volatility due to a Bayesian learning procedure. Starting…
In this paper a time-fractional Black-Scholes model (TFBSM) is considered to study the price change of the underlying fractal transmission system. We develop and analyze a numerical method to solve the TFBSM governing European options. The…
Options financial instruments designed to protect investors from the stock market randomness. In 1973, Fisher Black, Myron Scholes and Robert Merton proposed a very popular option pricing method using stochastic differential equations…
Option pricing models, essential in financial mathematics and risk management, have been extensively studied and recently advanced by AI methodologies. However, American option pricing remains challenging due to the complexity of…
We propose a versatile Monte-Carlo method for pricing and hedging options when the market is incomplete, for an arbitrary risk criterion (chosen here to be the expected shortfall), for a large class of stochastic processes, and in the…
Options have provided a field of much study because of the complexity involved in pricing them. The Black-Scholes equations were developed to price options but they are only valid for European styled options. There is added complexity when…
In this work we present an analytical model, based on the path-integral formalism of Statistical Mechanics, for pricing options using first-passage time problems involving both fixed and deterministically moving absorbing barriers under…
There is a well developed framework, the Black-Scholes theory, for the pricing of contracts based on the future prices of certain assets, called options. This theory assumes that the probability distribution of the returns of the underlying…
We consider a portfolio with call option and the corresponding underlying asset under the standard assumption that stock-market price represents a random variable with lognormal distribution. Minimizing the variance (hedging risk) of the…
This paper examines the valuation of a generalized American-style option known as a Game-style call option in an infinite time horizon setting. The specifications of this contract allow the writer to terminate the call option at any point…