Option Pricing in a Fractional Brownian Motion Environment

The purpose of this paper is to obtain a fractional Black-Scholes formula for the price of an option for every t in [0,T], a fractional Black-Scholes equation and a risk-neutral valuation theorem if the underlying is driven by a fractional Brownian motion BH (t), 1/2fractional Brownian motion, fractional Black-Scholes market, quasiconditional expectation

Modeling Heavy-Tailed Stock Index Returns Using the Generalized Hyperbolic Distribution

In the present study, we estimate the parameters of the Generalized Hyperbolic Distribution for a series of stock index returns including the Romanian BETC and indexes from other two Eastern European countries, Hungary and the Czech Republic. Using different econometric techniques, we investigate whether the estimated Generalized Hyperbolic Distribution is an appropriate approximation for the empirical distribution computed by non-parametric kernel econometric methods. The main finding of the analysis is that the probability density function of the estimated Generalized Hyperbolic Distribution represents a very close approximation (at least up to the 4th order term) of the empirical probability distribution function.Generalized Hyperbolic Distribution, heavy-tailed returns, non-parametric density estimation

Pricing European and Barrier Options in the Fractional Black-Scholes Market

The aim of this paper is to obtain the valuation formulas for European and barrier options if the underlying of the option contract is supposed to be driven by a fractional Brownian motion with Hurst parameter greater than 0.5. The paper is build upon the framework developed in Necula (2007) for the valuation of derivative products in the fractional Black-Scholes market. We also obtain a reflection principle for the fractional Brownian motion.fractional Brownian motion, fractional Black-Scholes market, the reflection principle for the fractional Brownian motion, mathematical finance, European option, barrier option

Barrier Options and a Reflection Principle of the Fractional Brownian Motion

The purpose of this paper is to obtain the price of the barrier options in a fractional Brownian motion environment in the special case of zero interest rate. As a consequence we derive a reflection principle for the fractional Brownian motion.fractional Brownian motion, fractional Black-Scholes market, quasiconditional expectation

Asset Pricing in a Two-Country Discontinuous General Equilibrium Model

The aim of this paper is to develop a framework for asset pricing in a continuous time general equilibrium model for a two country Lucas type economy. The model assumes that the output in the two countries follows a jump-diffusion stochastic process characterized by constant growth rates and volatilities and by log-normal amplitude of the jumps. Using this specification we deduce the fundamental evaluation equations for financial assets as well as a formula for the price of exchange rate options in this economy.general equilibrium model, two-country Lucas economy, exchange rate, risk premium, jump-diffusion

A Two-Country Discontinuous General Equilibrium Model

The aim of this paper is to develop a continuous time general equilibrium model for a two country Lucas type economy. The model assumes that the output in the two countries follows a jump-diffusion stochastic process. We obtain the results concerning the evaluation of financial assets, the determination of the exchange rate, of the interest rate, and of the risk premium in this two-country economy.general equilibrium model, two-country Lucas economy, exchange rate, risk premium, jump-diffusion

Modeling the Dependency Structure of Stock Index Returns using a Copula Function Approach

In the present study we assess the dependency structure between stock indexes by econometrically estimating the empirical copula function and the parameters of various parametric copula functions. The main finding is that the t-copula and the Gumbel-Clayton mixture copula are the most appropriate copula functions to capture the dependency structure of two financial return series. With the dependency structure given by the estimated copula functions we quantify the efficient portfolio frontier using as a risk measure CVaR (Conditional VaR) computed by Monte Carlo simulation. We find that in the case of using normal distributions for modeling individual returns the market risk is underestimated no mater what copula function is employed to capture the dependency structure.copula functions, copula mixtures, the efficient portfolio frontier, Conditional VAR, Monte Carlo simulation

A Framework for Derivative Pricing in the Fractional Black-Scholes Market

The aim of this paper is to develop a framework for evaluating derivatives if the underlying of the derivative contract is supposed to be driven by a fractional Brownian motion with Hurst parameter greater than 0.5. For this purpose we first prove some results regarding the quasi-conditional expectation, especially the behavior to a Girsanov transform. We obtain the risk-neutral valuation formula and the fundamental evaluation equation in the case of the fractional Black-Scholes market.fractional Brownian motion, fractional Black-Scholes market, quasiconditional expectation, mathematical finance, contingent claim

A model and framework for reliable build systems

Reliable and fast builds are essential for rapid turnaround during development and testing. Popular existing build systems rely on correct manual specification of build dependencies, which can lead to invalid build outputs and nondeterminism. We outline the challenges of developing reliable build systems and explore the design space for their implementation, with a focus on non-distributed, incremental, parallel build systems. We define a general model for resources accessed by build tasks and show its correspondence to the implementation technique of minimum information libraries, APIs that return no information that the application doesn't plan to use. We also summarize preliminary experimental results from several prototype build managers

Tackling Dynamic Vehicle Routing Problem with Time Windows by means of Ant Colony System

The Dynamic Vehicle Routing Problem with Time Windows (DVRPTW) is an extension of the well-known Vehicle Routing Problem (VRP), which takes into account the dynamic nature of the problem. This aspect requires the vehicle routes to be updated in an ongoing manner as new customer requests arrive in the system and must be incorporated into an evolving schedule during the working day. Besides the vehicle capacity constraint involved in the classical VRP, DVRPTW considers in addition time windows, which are able to better capture real-world situations. Despite this, so far, few studies have focused on tackling this problem of greater practical importance. To this end, this study devises for the resolution of DVRPTW, an ant colony optimization based algorithm, which resorts to a joint solution construction mechanism, able to construct in parallel the vehicle routes. This method is coupled with a local search procedure, aimed to further improve the solutions built by ants, and with an insertion heuristics, which tries to reduce the number of vehicles used to service the available customers. The experiments indicate that the proposed algorithm is competitive and effective, and on DVRPTW instances with a higher dynamicity level, it is able to yield better results compared to existing ant-based approaches.Comment: 10 pages, 2 figure