Valuing options in Heston's stochastic volatility model: Another analytical approach

We are concerned with the valuation of European options in Heston's stochastic volatility model with correlation. Based on Mellin transforms we present new closed-form solutions for the price of European options and hedging parameters. In contrast to Fourier-based approaches where the transformation variable is usually the log-stock price at maturity, our framework focuses on transforming the current stock price. Our solution has the nice feature that similar to the approach of Carr and Madan (1999) it requires only a single integration. We make numerical tests to compare our results to Heston's solution based on Fourier inversion and investigate the accuracy of the derived pricing formulae. --Stochastic volatility,European option,Mellin transform

Pricing American options with Mellin transforms

Mellin transforms in option pricing theory were introduced by Panini and Srivastav (2004). In this contribution, we generalize their results to European power options. We derive Black-Scholes-Merton-like valuation formulas for European power put options using Mellin transforms. Thereafter, we restrict our attention to plain vanilla options on dividend-paying stocks and derive the integral equations to determine the free boundary and the price of American put options using Mellin transforms. We recover a result found by Kim (1990) regarding the optimal exercise price of American put options at expiry and prove the equivalence of integral representations herein, the representation derived by Kim (1990), Jacka (1991), and by Carr et al. (1992). Finally, we extend the results obtained in Panini and Srivastav (2005) and show how the Mellin transform approach can be used to derive the valuation formula for perpetual American put options on dividend-paying stocks. --Mellin transform,Power option,American put option,Free boundary,Integral representation

On modified Mellin transforms, Gauss-Laguerre quadrature, and the valuation of American call options

We extend a framework based on Mellin transforms and show how to modify the approach to value American call options on dividend paying stocks. We present a new integral equation to determine the price of an American call option and its free boundary using modi ed Mellin transforms. We also show how to derive the pricing formula for perpetual American call options using the new framework. A recovery of a result due to Kim (1990) regarding the optimal exercise price at expiry is also presented. Finally, we apply Gauss-Laguerre quadrature for the purpose of an efficient and accurate numerical valuation. --Modified Mellin transform,American call option,Integral representation

Textile structures modeled on a spider's net

Innovative textile fabrics modelled on the structure of a spider web can find application in the reinforcing of composites in conditions of where a centrifugal force occurs, for example rotational discs. At the Institute of Architecture of Textile at the Technical University of Łódź research work is carried out on mechanised production of woven fabrics whose struc- ture is modelled on a spider webweb. The paper presents a review of textile techniques and technologies from the point of view of their usefulness for producing fabrics of a flat round net type structure modelled on the structure of a spider web.There is also an analysis of the mechanical properties of the different textile structures from the point of view of fulfilling the requirements to operate in conditions which are affected by a centrifugal force

Adjuncts and the Chimera of Academic Freedom

The last 40 years have seen a dramatic shift in the hiring, evaluation and promotional structures prevalent in higher education. While the model of a largely full time, tenure-track faculty continues to be the ideal of most academic institutions, economic, political and social changes have eroded that model. A substantial percentage, typically a majority, of college and university faculty are now hired on a contingent or part-time basis, with fiscal and other conditions determining job security, compensation, professional advancement, and an opportunity to participate in governance of departments and institutions. This paper examines the unseen impact that such hiring practices have on professionalism and academic freedoms, not only for contingent faculty themselves but for faculty as a whole. We conclude that the current, two-class faculty system not only erodes collegiality and cohesion, but inhibits the quest for knowledge, wisdom and social justice that are a core mission of higher education

A series of Ramanujan, two-term dilogarithm identities and some Lucas series

We study an elementary series that can be considered a relative of a series studied by Ramanujan in Part 1 of his Lost Notebooks. We derive a closed form for this series in terms of the inverse hyperbolic arctangent and the polylogarithm. Special cases will follow in terms of the Riemann zeta and the alternating Riemann zeta function. In addition, some trigonometric series will be expressed in terms of the Clausen functions. Finally, a range of new two-term dilogarithm identities will be proved and some difficult series involving Lucas numbers will be evaluated in closed form.Comment: 26 pages, no figures or table

Examination of Eco-Behavioral Assessments Designed for Understanding Complex Behaviors and Environments.

Second-generation intervention research requires methods for overcoming challenges to understanding complex learning ecologies and interactions of students. Eco-behavioral assessments (EBAs) are one solution to past intervention research challenges. EBAs record the effects of ecological variables in students’ behavior and daily interactions. The utility of EBAs in second-generation research has increased substantially. Numerous EBAs now exist for use with all ages of learners and provide a valid, reliable, and cost effective method for intervention research. This paper examines 18 EBAs as well as software systems designed to support and enhance the use of EBAs. The examination serves as a comprehensive resource to better understand how EBAs can be used in answering complex questions about students’ learning and for advancing second-generation research

Balancing polynomials, Fibonacci numbers and some new series for π\pi

We evaluate some types of infinite series with balancing and Lucas-balancing polynomials in closed form. These evaluations will lead to some new curious series for $\pi$ involving Fibonacci and Lucas numbers. Our findings complement those of Castellanos from 1986 and 1989.Comment: 16 pages, 5 table