Related papers: Adaptive-Wave Alternative for the Black-Scholes Op…
This paper presents a new prediction model for time series data by integrating a time-varying Geometric Brownian Motion model with a pricing mechanism used in financial engineering. Typical time series models such as Auto-Regressive…
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…
This paper concerns a local volatility model in which volatility takes two possible values, and the specific value depends on whether the underlying price is above or below a given threshold value. The model is known, and a number of…
Option prices encode the market's collective outlook through implied density and implied volatility. An explicit link between implied density and implied volatility translates the risk-neutrality of the former into conditions on the latter…
Predicting volatility is important for asset predicting, option pricing and hedging strategies because it cannot be directly observed in the financial market. The Black-Scholes option pricing model is one of the most widely used models by…
The financial rogue waves are reported analytically in the nonlinear option pricing model due to Ivancevic, which is nonlinear wave alternative of the Black-Scholes model. These solutions may be used to describe the possible physical…
This paper studies the pricing of European-style Asian options when the price dynamics of the underlying risky asset are assumed to follow a Markov- modulated geometric Brownian motion; that is, the appreciation rate and the volatility of…
Closed form option pricing formulae explaining skew and smile are obtained within a parsimonious non-Gaussian framework. We extend the non-Gaussian option pricing model of L. Borland (Quantitative Finance, {\bf 2}, 415-431, 2002) to include…
This paper studies the pricing problem in which the underlying asset follows a non-Markovian stochastic volatility model. Classical partial differential equation methods face significant challenges in this context, as the option prices…
This paper is concerned with nonlinear filtering of the coefficients in asset price models with stochastic volatility. More specifically, we assume that the asset price process $S=(S_{t})_{t\geq0}$ is given by \[ dS_{t}=m(\theta_{t})S_{t}…
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 consider a non-stochastic online learning approach to price financial options by modeling the market dynamic as a repeated game between the nature (adversary) and the investor. We demonstrate that such framework yields analogous…
In the classical model of stock prices which is assumed to be Geometric Brownian motion, the drift and the volatility of the prices are held constant. However, in reality, the volatility does vary. In quantitative finance, the Heston model…
The shortcomings of the popular Black-Scholes-Merton (BSM) model have led to models which could more accurately model the behavior of the underlying assets in energy markets, particularly in electricity and future oil prices. In this paper…
Based on the analog between the stochastic dynamics and quantum harmonic oscillator, we propose a market force driving model to generalize the Black-Scholes model in finance market. We give new schemes of option pricing, in which we can…
In this paper we consider a new mathematical extension of the Black-Scholes model in which the stochastic time and stock share price evolution is described by two independent random processes. The parent process is Brownian, and the…
This paper is concerned with nonlinear filtering of the coefficients in asset price models with stochastic volatility. More specifically, we assume that the asset price process $ S=(S_{t})_{t\geq0} $ is given by \[…
This paper proposes a data-driven approach, by means of an Artificial Neural Network (ANN), to value financial options and to calculate implied volatilities with the aim of accelerating the corresponding numerical methods. With ANNs being…
The short maturity limit $T\to 0$ for the implied volatility of an Asian option in the Black-Scholes model is determined by the large deviations property for the time-average of the geometric Brownian motion. In this note we derive the…
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…