Related papers: Time-independent pricing of options in range bound…
Traders and investors involved in an option contract having the underlying stock in range bound are likely to lose their initial investment. Timing in buying an option contract is of capital importance. In a recent article [1] the…
A new mathematical model for the Black-Scholes equation is proposed to forecast option prices. This model includes new interval for the price of the underlying stock as well as new initial and boundary conditions. Conventional notions of…
We show how the prices of options can be determined with the help of double-fractional differential equation in such a way that their inclusion in a portfolio of stocks provides a more reliable hedge against dramatic price drops that the…
Option contracts can be valued by using the Black-Scholes equation, a partial differential equation with initial conditions. An exact solution for European style options is known. The computation time and the error need to be minimized…
It is well-known that the Black-Scholes formula has been derived under the assumption of constant volatility in stocks. In spite of evidence that this parameter is not constant, this formula is widely used by financial markets. This paper…
The aim of this paper is to present a simple stochastic model that accounts for the effects of a long-memory in volatility on option pricing. The starting point is the stochastic Black-Scholes equation involving volatility with long-range…
The Black-Scholes formula for pricing options on stocks and other securities has been generalized by Merton and Garman to the case when stock volatility is stochastic. The derivation of the price of a security derivative with stochastic…
Option pricing is an integral part of modern financial risk management. The well-known Black and Scholes (1973) formula is commonly used for this purpose. This paper is an attempt to extend their work to a situation in which the…
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…
We investigate qualitative and quantitative behavior of a solution of the mathematical model for pricing American style of perpetual put options. We assume the option price is a solution to the stationary generalized Black-Scholes equation…
Black-Scholes implied volatility is a quantile. The insight follows from the normalized option price being a probability on the variance scale, with the inverse Gaussian distribution providing the link. It enables analytically exact and…
In this paper we investigate a nonlinear generalization of the Black-Scholes equation for pricing American style call options in which the volatility term may depend on the underlying asset price and the Gamma of the option. We propose a…
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…
Writing the article-Time independent pricing of options in range bound markets; the question in the title came naturally to my mind. It is stated, in the above article, that in certain market conditions the stock price is subjected to an…
Black-Scholes (BS) is the standard mathematical model for option pricing in financial markets. Option prices are calculated using an analytical formula whose main inputs are strike (at which price to exercise) and volatility. The BS…
The price of a stock will rarely follow the assumed model and a curious investor or a Regulatory Authority may wish to obtain a probability model the prices support. A risk neutral probability ${\cal P}^*$ for the stock's price at time $T$…
One of the shortcomings of the Black and Scholes model on option pricing is the assumption that trading of the underlying asset does not affect the price of that asset. This assumption can be fulfilled only in perfectly liquid markets.…
The classical linear Black--Scholes model for pricing derivative securities is a popular model in financial industry. It relies on several restrictive assumptions such as completeness, and frictionless of the market as well as the…
One of the most discussed problems in the financial world is stock option pricing. The Black-Scholes Equation is a Parabolic Partial Differential Equation which provides an option pricing model. The present work proposes an approach based…
This paper presents a derivation of the explicit price for the perpetual American put option in the Black-Scholes model, time-capped by the first drawdown epoch beyond a predefined level. We demonstrate that the optimal exercise strategy…