Ciprian Necula

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), 1/2

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.

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.

LONG MEMORY IN EASTERN EUROPEAN FINANCIAL MARKETS RETURNS

Abstract The paper examines the long memory property of stock returns and its implications using daily index returns for eight CEE emerging markets: Romania, Hungary, Czech Republic, Poland, Slovenia, Bulgaria, Slovakia, and Croatia. Several nonparametric methods for testing for long memory are employed, as well as parametric long memory models. The ARFIMA-FIGARCH model seems the most appropriate specification since the nonlinearity tests can not reject the null of independent and identically distributed residuals, implying that this specification accounts for the nonlinearity in the data. The estimated fractional differencing parameter is statistically significant in seven of the eight emerging economies employed in the study, suggesting the presence of long memory in the returns in these financial markets.

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.

Herding and Stochastic Volatility

In this paper we develop a one-factor non-affine stochastic volatility option pricing model where the dynamics of the underlying is endogenously determined from micro-foundations. The interaction and herding of the agents trading the underlying asset induce an amplification of the volatility of the asset over the volatility of the fundamentals. Although the model is non-affine, a closed form option pricing formula can still be derived by using a Gauss-Hermite series expansion methodology. The model is calibrated using S&P 500 index options for the period 1996-2013. When its results are compared to some benchmark models we find that the new non-affine one-factor model outperforms the affine one-factor Heston model and it is competitive, especially out-of-sample, with the affine two-factor double Heston model.

The Dynamics of Heterogeneity and Asset Prices

In the context of a continuous-time pure-exchange economy model, the paper develops a novel methodology, based on measure-valued stochastic processes, for analyzing the evolution of heterogeneity in a tractable manner and studying its impact on asset prices. The agents in the economy differ with respect to impatience, risk aversion, beliefs about the growth rate of output, and to the rules for updating beliefs. The heterogeneity itself is described by a single object, a measure, and its dynamics by a measure-valued stochastic process. A key contribution of the paper consists in obtaining a closed form formula for the stock price in the case in which preferences are homogeneous with the risk aversion parameter given by a natural number. We also synthesize and generalize existing results about the equilibrium in heterogeneous pure-exchange complete markets economies and we highlight the importance of the endogenously determined risk tolerance weighted consumption distribution as a key ingredient in driving the equilibrium variables.

An Approximation of an Equivalent European Payoff for the American Put Option

Is the American put option simply an incognito European one? In this paper, we develop a numerical procedure, in the context of the Black-Scholes model, to approximate the payoff of a European type option that generates prices that are equal to the prices of the American put option in the continuation region. The resulting equivalent European payoff is a sum of power payoffs, and therefore the price and the hedging indicators can be computed in closed form. For a given set of model parameters (interest rate, dividend rate and volatility) the computation of the equivalent European payoff reduces to solving a linear optimization problem. We conduct a numerical experiment spanning a wide range of model parameters and contract characteristics and, overall, the method produces American option prices with a relative RMSE of 0.01% compared to a benchmark.

The Impact of Cointegration on Commodity Spread Options

In this work we explore the implications of cointegration in a system of commodity prices on the premiums of options written on various spreads on the futures prices of these commodities. We employ a parsimonious, yet comprehensive model for cointegration in a system of commodity prices. The model has an exponential affine structure and is flexible enough to allow for an arbitrary number of cointegration relationships. We conduct an extensive simulation study on pricing spread options. We argue that cointegration creates an upward sloping term structure of correlation, that in turn lowers the volatility of spreads and consequently the price of options on them.

A Generalized Bachelier Formula for Pricing Basket and Spread Options

In this paper we propose a closed-form pricing formula for European basket and spread options. Our approach is based on approximating the risk-neutral probability density function of the terminal value of the basket using a Gauss-Hermite series expansion around the Gaussian density. The new method is quite general as it can be applied for a basket with a large number of assets and for all dynamics where the joint characteristic function of log-returns is known in closed form. We provide a simulation study to show the accuracy and the speed of our methodology.