Related papers: The pricing of lookback options and binomial appro…
We consider the problem of pricing perpetual American options written on dividend-paying assets whose price dynamics follow a multidimensional Black and Scholes model. For convex Lipschitz continuous reward functions, we give a…
We reconsider the problem of option pricing using historical probability distributions. We first discuss how the risk-minimisation scheme proposed recently is an adequate starting point under the realistic assumption that price increments…
We consider approximate pricing formulas for European options based on approximating the logarithmic return's density of the underlying by a linear combination of rescaled Hermite polynomials. The resulting models, that can be seen as…
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…
In this article, a compact finite difference method is proposed for pricing European and American options under jump-diffusion models. Partial integro-differential equation and linear complementary problem governing European and American…
The limitations of the classical Black-Scholes model are examined by comparing calculated and actual historical prices of European call options on stocks from several sectors of the S&P 500. Persistent differences between the two prices…
This paper investigates the pricing of European-style lookback options when the price dynamics of the underlying risky asset are assumed to follow a Markov-modulated Geo-metric Brownian motion; that is, the appreciation rate and the…
Using spectral decomposition techniques and singular perturbation theory, we develop a systematic method to approximate the prices of a variety of options in a fast mean-reverting stochastic volatility setting. Four examples are provided in…
We develop a quantum algorithm to price discretely monitored lookback options in the Black-Scholes framework using imaginary time evolution. By rewriting the pricing PDE as a Schrodinger-type equation, the problem becomes the imaginary time…
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…
In the framework of Black-Scholes-Merton model of financial derivatives, a path integral approach to option pricing is presented. A general formula to price European path dependent options on multidimensional assets is obtained and…
This paper presents a novel way to predict options price for one day in advance, utilizing the method of Quasi-Reversibility for solving the Black-Scholes equation. The Black-Scholes equation solved forwards in time with Tikhonov…
The mean objective of this paper is to derive an explicit formula for a price of an European option associated to the underlying delayed stock price which follows a linear differential equation with a general delay in the drift term. We use…
Following the foundational work of the Black--Scholes model, extensive research has been developed to price the option by addressing its underlying assumptions and associated pricing biases. This study introduces a novel framework for…
Assuming that price of the underlying stock is moving in range bound, the Black-Scholes formula for options pricing supports a separation of variables. The resulting time-independent equation is solved employing different behavior of the…
In this paper, we present a reduced basis method for pricing European and American options based on the Black-Scholes and Heston model. To tackle each model numerically, we formulate the problem in terms of a time dependent variational…
We consider the binomial approximation of the American put price in the Black-Scholes model (with continuous dividend yield). Our main result is that the error of approximation is $O((ln n) $\alpha$ /n)$ where n is the number of time…
The objective of this paper is to introduce the theory of option pricing for markets with informed traders within the framework of dynamic asset pricing theory. We introduce new models for option pricing for informed traders in complete…
Here we develop an option pricing method based on Legendre series expansion of the density function. The key insight, relying on the close relation of the characteristic function with the series coefficients, allows to recover the density…
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…