Related papers: Asian Basket Spread Options: A New Approximation B…
We study the numerical evaluation of several functions appearing in the small time expansion of the distribution of the time-integral of the geometric Brownian motion as well as its joint distribution with the terminal value of the…
The true probability of a European call option to achieve positive return is investigated under the Black-Scholes model. It is found that the probability is determined by those market factors appearing in the BS formula, besides the growth…
We analyze and calculate the early exercise boundary for a class of stationary generalized Black-Scholes equations in which the volatility function depends on the second derivative of the option price itself. A motivation for studying the…
In this paper we present some results on Geometric Asian option valuation for affine stochastic volatility models with jumps. We shall provide a general framework into which several different valuation problems based on some average process…
We consider a non-Gaussian option pricing model, into which the underlying log-price is assumed to be driven by an $\alpha$-stable distribution. We remove the a priori divergence of the model by introducing a Mellin regularization for the…
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 work, we propose an algorithm to price American options by directly solving the dual minimization problem introduced by Rogers. Our approach relies on approximating the set of uniformly square integrable martingales by a finite…
The paper investigates the performance of the European option price when the log asset price follows a rich class of Generalized Tempered Stable (GTS) distribution. The GTS distribution is an alternative to Normal distribution and…
We present an approximation method based on the mixing formula (Hull & White 1987, Romano & Touzi 1997) for pricing European options in Barndorff-Nielsen and Shephard models. This approximation is based on a Taylor expansion of the option…
We present a new approximation scheme for the price and exercise policy of American options. The scheme is based on Hermite polynomial expansions of the transition density of the underlying asset dynamics and the early exercise premium…
A growing body of literature suggests that heavy tailed distributions represent an adequate model for the observations of log returns of stocks. Motivated by these findings, here we develop a discrete time framework for pricing of European…
Market illiquidity, feedback effects, presence of transaction costs, risk from unprotected portfolio and other nonlinear effects in PDE based option pricing models can be described by solutions to the generalized Black-Scholes parabolic…
Asian option, as one of the path-dependent exotic options, is widely traded in the energy market, either for speculation or hedging. However, it is hard to price, especially the one with the arithmetic average price. The traditional trading…
We invert the Black-Scholes formula. We consider the cases low strike, large strike, short maturity and large maturity. We give explicitly the first 5 terms of the expansions. A method to compute all the terms by induction is also given. At…
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…
The paper develops a new class of financial market models. These models are based on generalized telegraph processes: Markov random flows with alternating velocities and jumps occurring when the velocities are switching. While such markets…
We describe general multilevel Monte Carlo methods that estimate the price of an Asian option monitored at $m$ fixed dates. Our approach yields unbiased estimators with standard deviation $O(\epsilon)$ in $O(m + (1/\epsilon)^{2})$ expected…
Path integral techniques for the pricing of financial options are mostly based on models that can be recast in terms of a Fokker-Planck differential equation and that, consequently, neglect jumps and only describe drift and diffusion. We…
As a rigorous statistical approach, statistical Taylor expansion extends the conventional Taylor expansion by replacing precise input variables with random variables of known distributions and sample counts to compute the mean, the…
A classical inventory problem is studied from the perspective of embedded options, reducing inventory-management to the design of optimal contracts for forward delivery of stock (commodity). Financial option techniques \`{a} la…