Fractional diffusion models of option prices in markets with jumps

Most of the recent literature dealing with the modeling of financial assets assumes that the underlying dynamics of equity prices follow a jump process or a Lévy process. This is done to incorporate rare or extreme events not captured by Gaussian models. Of those financial models proposed, the most interesting include the CGMY, KoBoL and FMLS. All of these capture some of the most important characteristics of the dynamics of stock prices. In this article we show that for these particular Lévy processes, the prices of financial derivatives, such as European-style options, satisfy a fractional partial differential equation (FPDE). As an application, we use numerical techniques to price exotic options, in particular barrier options, by solving the corresponding FPDEs derived.     

Hybrid artificial neural networks for efficient valuation of real options and financial derivatives

A hybrid valuation methodology is proposed and tested for improving the efficiency of contingent claims pricing by combining Artificial Neural Networks (ANN) and conventional parametric option pricing techniques. With one application on financial derivatives and one on real options the methods superiority is demonstrated. The resulting efficiency is instrumental for real time applications.MSC code: 90-08 Acknowledgements: Both authors are thankful for partial financial support to the HERMES European Center of Excellence on Computational Finance and Economics of the University of Cyprus and a University of Cyprus grant for research in ANNs and Derivatives, and to the anonymous referees for their helpful comments and discussions.     

A Pricing Model for American Options with Gaussian Interest Rates

In this paper we introduce a new methodology to price American put options under stochastic interest rates. We derive an analytic approximation that can be evaluated very fast and is fairly accurate. The method uses the so-called forward risk adjusted measure to derive analytic prices. We show that for American puts the correlation between the stock price and the interest rate has different influences on European option values and early exercise premiums.     

The Pietra term structures of financial assets

This paper explores an elemental connection between call options-the most commonly tradable financial derivatives, implied volatility term structures-critical “market information” emanating from call-option prices, and the Pietra index-a quantitative economic measure of societal egalitarianism. Our study: (i) unveils an intrinsic “Pietra structure” of call-option prices; (ii) introduces the notion of the “Pietra term structures” of financial assets; (iii) describes the probabilistic meaning of the Pietra term structures; (iv) establishes an explicit nonlinear one-to-one mapping between the Pietra term structures and the implied volatility term structures of financial assets. The results presented in this paper provide a deep insight into the econophysics of call options and implied volatility term structures.     

Approximation of bivariate copulas by patched bivariate Fréchet copulas

Bivariate Fréchet (BF) copulas characterize dependence as a mixture of three simple structures: comonotonicity, independence and countermonotonicity. They are easily interpretable but have limitations when used as approximations to general dependence structures. To improve the approximation property of the BF copulas and keep the advantage of easy interpretation, we develop a new copula approximation scheme by using BF copulas locally and patching the local pieces together. Error bounds and a probabilistic interpretation of this approximation scheme are developed. The new approximation scheme is compared with several existing copula approximations, including shuffle of min, checkmin, checkerboard and Bernstein approximations and exhibits better performance, especially in characterizing the local dependence. The utility of the new approximation scheme in insurance and finance is illustrated in the computation of the rainbow option prices and stop-loss premiums.     

On the explicit evaluation of the Geometric Asian options in stochastic volatility models with jumps

In the present paper we provide a semiexplicit valuation formula for Geometric Asian options, with fixed and floating strike under continuous monitoring, when the underlying stock price process exhibits both stochastic volatility and jumps. More precisely, we shall work in the Barndorff-Nielsen and Shephard (BNS) model framework. We shall provide some numerical illustrations of the results obtained.     

A stochastic programming model using an endogenously determined worst case risk measure for dynamic asset allocation

We present a new approach to asset allocation with transaction costs. A multiperiod stochastic linear programming model is developed where the risk is based on the worst case payoff that is endogenously determined by the model that balances expected return and risk. Utilizing portfolio protection and dynamic hedging, an investment portfolio similar to an option-like payoff structure on the initial investment portfolio is characterized. The relative changes in the expected terminal wealth, worst case payoff, and risk aversion, are studied theoretically and illustrated using a numerical example. This model dominates a static mean-variance model when the optimal portfolios are evaluated by the Sharpe ratio. Received: August 15, 1999 / Accepted: October 1, 2000?Published online December 15, 2000     

模拟静电场实验中导电介质的选择

通过比较3种静电场描绘仪器的实验结果,分析误差产生的原因,指出选择导电介质应注意的问题。     

一种基于互补判断矩阵逆判问题的新方法

针对群决策中互补判断矩阵的逆判问题,给出一种新的分析方法.方法通过对互补判断矩阵的导出矩阵向量化后进行偏差比较来对评判专家的评判水平进行排序,给出了对评判专家分类的模糊数学方法,并通过算例验证该方法的实用性和有效性.