Analytic Pricing of Contingent Claims Under the Real-World Measure

This article derives a series of analytic formulae for various contingent claims under the real-world probability measure using the stylised minimal market model (SMMM). This model provides realistic dynamics for the growth optimal portfolio (GOP) as a well-diversified equity index. It captures both leptokurtic returns with correct tail properties and the leverage effect. Under the SMMM, the discounted GOP takes the form of a time-transformed squared Bessel process of dimension four. From this property, one finds that the SMMM possesses a special and interesting relationship to non-central chi-square random variables with zero degrees of freedom. The analytic formulae derived under the SMMM include options on the GOP, options on exchange prices and options on zero-coupon bonds. For options on zero-coupon bonds, analytic prices facilitate efficient calculation of interest rate caps and floors.benchmark approach; real-world pricing; growth optimal portfolio; minimal market model; zero-coupon bonds; exchange prices; interest rate caps and floors

Two-Factor Model for Low Interest Rate Regimes

This paper derives a two factor model for the term structure of interest rates that segments the yield curve in a natural way. The first factor involves modelling a non-negative short rate process that primarily determines the early part of the yield curve and is obtained as a truncated Gaussian short rate. The second factor mainly influences the later part of the yield curve via the market index. The market index proxies the growth optimal portfolio (GOP) and is modelled as a squared Bessel process of dimension four. Although this setup can be applied to any interest rate environment, this study focuses on the difficult but important case where the short rate stays close to zero for a prolonged period of time. For the proposed model, an equivalent risk neutral martingale measure is niether possible nor required. Hence we use the benchmark approach where the GOP is chosen as numeraire. Fair derivative prices are then calculated via conditional expectations under the real world probability measure. Using this methodology we derive pricing functions for zero coupon bonds and options on zero coupon bonds. The proposed model naturally generates yield curve shapes commonly observed in the market. More importantly, the model replicates the key features of the interest rate cap market for economies with low interest rate regimes. In particular, the implied volatility term structure displays a consistent downward slope from extremely high levels of volatility together with a distinct negative skew.interest rate term structure; growth optimal portfolio; fair pricing; total market price for risk; interest rate caps

Benchmarking and Fair Pricing Applied to Two Market Models

This paper considers a market containing both continuous and discrete noise. Modest assumptions ensure the existence of a growth optimal portfolio. Non-negative self-financing trading strategies, when benchmarked by this portfolio, are local martingales under the real-world measure. This justifies the fair pricing approach, which expresses derivative prices in terms of real-world conditional expectations of benchmarked payoffs. Two models for benchmarked primary security accounts are presented, and fair pricing formulas for some common contingent claims are derived.growth optimal portfolio; benchmark approach; fair pricing; Merton model; minimal market model

Just Look at her! : Sporting Bodies as Athletic Resistance and the Limits of Sport Norms in the Case of Caster Semenya

Using the American sport media’s treatment of South African runner Caster Semenya, this article explores how in the course of defending Caster Semenya the American sport media presented a rigorous challenge to traditional conceptions of sex and gender. Yet these rhetorical efforts to deconstruct sex and gender binaries were undermined by the specific ways in which Semenya’s dual performances—athletic and gender—were visually depicted. A close reading and analysis of US sports media coverage of Caster Semenya provide an opportunity to explore the ways in which the norms of sport may foster progressive treatment of athletes whose genders do not fit comfortably within the existing, traditional expectations of what men and women should be like. At the same time, however, I wish to suggest that both discursive and visual rhetoric are limited in how much they can use such sports norms when ontological questions about the normal, the natural, and the body are at stake. By paying particular attention to the interplay between the linguistic, the visual, and the performative, I hope to show that even the most sincere efforts to complicate sex and gender within the framework of sport have significant limitations

Exploring Men’s Motivations for Studying, and not Studying, Abroad

A long-standing trend in collegiate study abroad experiences has been the continual underrepresentation of key student demographics. One of the most persistent of these disparities has been the lack of men studying abroad. Between the 1996 and 2007 academic years, men’s participation rate in study abroad experiences consistently hovered at 35%. Female students, in other words, participated in study abroad at a rate nearly twice that of their male peers. This research project was designed around two hypotheses – that ethnocentrism influenced men’s decisions to study abroad; and that racial or ethnic prejudice influenced men’s decisions to study abroad. In addition, data collection was intended to explore what other factors men might provide behind their decision to study abroad or not

Making the Boys Cry: The Performative Dimensions of Fluid Gender

This essay examines how young girls who participate in combat sports such as wrestling, a traditionally male stronghold, perform continually shifting gender identities that interweave physical traits and behaviors typically coded as masculine or feminine. Drawing upon auto-ethnographic and ethnographic methodologies, I demonstrate how a study of actual lived body experience grounded in a fluid conception of gender is able to remain sensitive to the unique performative gender work being done while providing a critical interrogation of the moments in which the performance of gender is inscribed as nonconformative. I suggest that if we wish to understand the gender dynamics involved in athletic competition, it is necessary to approach gender as a fluid, rather than solid, concept