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The aim of this work is to introduce a new stochastic volatility model for equity derivatives. To overcome some of the well-known problems of the Heston model, and more generally of the affine models, we define a new specification for the…

This paper focuses on the pricing of continuous geometric Asian options (GAOs) under a multifactor stochastic volatility model. The model considers fast and slow mean reverting factors of volatility, where slow volatility factor is…

A nonlinear wave alternative for the standard Black-Scholes option-pricing model is presented. The adaptive-wave model, representing 'controlled Brownian behavior' of financial markets, is formally defined by adaptive nonlinear…

This study investigates enhancing option pricing by extending the Black-Scholes model to include stochastic volatility and interest rate variability within the Partial Differential Equation (PDE). The PDE is solved using the finite…

A unified analytical pricing framework with involvement of the shot noise random process has been introduced and elaborated. Two exactly solvable new models have been developed. The first model has been designed to value options. It is…

The present paper proposes a new framework for describing the stock price dynamics. In the traditional geometric Brownian motion model and its variants, volatility plays a vital role. The modern studies of asset pricing expand around…

We provide an European option pricing formula written in the form of an infinite series of Black Scholes type terms under double Levy jumps model, where both the interest rate and underlying price are driven by Levy process. The series…

This paper develops a European option pricing formula for fractional market models. Although there exist option pricing results for a fractional Black-Scholes model, they are established without accounting for stochastic volatility. In this…

We obtain a decomposition of the call option price for a very general stochastic volatility diffusion model extending the decomposition obtained by E. Al\`os in [2] for the Heston model. We realize that a new term arises when the stock…

Volatility clustering, long-range dependence, and non-Gaussian scaling are stylized facts of financial assets dynamics. They are ignored in the Black & Scholes framework, but have a relevant impact on the pricing of options written on…

The Black-Scholes model (sometimes known as the Black-Scholes-Merton model) gives a theoretical estimate for the price of European options. The price evolution under this model is described by the Black-Scholes formula, one of the most…

In this paper, we obtain the existence, uniqueness and positivity of the solution to delayed stochastic differential equations with jumps. This equation is then applied to model the price movement of the risky asset in a financial market…

Refining a discrete model of Cheuk and Vorst we obtain a closed formula for the price of a European lookback option at any time between emission and maturity. We derive an asymptotic expansion of the price as the number of periods tends to…

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 present two explicit rational formulae for Bachelier, or normal, implied volatility. The formulae take the option price, forward, strike, and expiry as inputs and return the implied normal volatility without iteration. They follow the…

We introduce a new method to price American options based on Chebyshev interpolation. In each step of a dynamic programming time-stepping we approximate the value function with Chebyshev polynomials. The key advantage of this approach is…

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…

We fit the volatility fluctuations of the S&P 500 index well by a Chi distribution, and the distribution of log-returns by a corresponding superposition of Gaussian distributions. The Fourier transform of this is, remarkably, of the Tsallis…

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…

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…