相关论文: Martingale Option Pricing

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…

In this paper, we address one of the main puzzles in finance observed in the stock market by proponents of behavioral finance: the stock predictability puzzle. We offer a statistical model within the context of rational finance which can be…

The aim of this paper is to introduce a new formalism for the deterministic analysis associated with backward stochastic differential equations driven by general c{\`a}dl{\`a}g martingales. When the martingale is a standard Brownian motion,…

In the standard Black-Scholes-Merton framework, dividends are represented as a continuous dividend yield and the pricing of Vanilla options on a stock is achieved through the well-known Black-Scholes formula. In reality however, stocks pay…

In this article, we study the rate of convergence of prices when a model is approximated by some simplified model. We also provide a method how explicit error formula for more general options can be obtained if such formula is available for…

The space of call price functions has a natural noncommutative semigroup structure with an involution. A basic example is the Black--Scholes call price surface, from which an interesting inequality for Black--Scholes implied volatility is…

We consider arbitrage free valuation of European options in Black-Scholes and Merton markets, where the general structure of the market is known, however the specific parameters are not known. In order to reflect this subjective uncertainty…

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…

The aim of this chapter is to show how option prices in jump-diffusion models can be computed using meshless methods based on Radial Basis Function (RBF) interpolation. The RBF technique is demonstrated by solving the partial…

We consider a generic market model with a single stock and with random volatility. We assume that there is a number of tradable options for that stock with different strike prices. The paper states the problem of finding a pricing rule that…

In this paper we provide a quantum Monte Carlo algorithm to solve multidimensional Black-Scholes PDEs with correlation for option pricing. The payoff function of the option is of general form and is only required to be continuous and…

We consider conditional-mean hedging in a fractional Black-Scholes pricing model in the presence of proportional transaction costs. We develop an explicit formula for the conditional-mean hedging portfolio in terms of the recently…

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…

This study deals with the problem of pricing European currency options in discrete time setting, whose prices follow the fractional Black Scholes model with transaction costs. Both the pricing formula and the fractional partial differential…

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…

An efficient computational algorithm to price financial derivatives is presented. It is based on a path integral formulation of the pricing problem. It is shown how the path integral approach can be worked out in order to obtain fast and…

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 develop a comprehensive mathematical framework for polynomial jump-diffusions in a semimartingale context, which nest affine jump-diffusions and have broad applications in finance. We show that the polynomial property is preserved under…

We investigate the relation between the fair price for European-style vanilla options and the distribution of short-term returns on the underlying asset ignoring transaction and other costs. We compute the risk-neutral probability density…

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…