SPINON BASIS FOR (sl2^)_k INTEGRABLE HIGHEST WEIGHT MODULES AND NEW CHARACTER FORMULAS

In this note we review the spinon basis for the integrable highest weight modules of sl2^ at levels k\geq1, and give the corresponding character formula. We show that our spinon basis is intimately related to the basis proposed by Foda et al. in the principal gradation of the algebra. This gives rise to new identities for the q-dimensions of the integrable modules.Comment: 9 pages, plain TeX + amssym.def, to appear in the proceedings of `Statistical Mechanics and Quantum Field Theory,' USC, May 16-21, 199

Mandelbrot's Extremism

In the sixties Mandelbrot already showed that extreme price swings are more likely than some of us think or incorporate in our models.A modern toolbox for analyzing such rare events can be found in the field of extreme value theory.At the core of extreme value theory lies the modelling of maxima over large blocks of observations and of excesses over high thresholds.The general validity of these models makes them suitable for out-of-sample extrapolation.By way of illustration we assess the likeliness of the crash of the Dow Jones on October 19, 1987, a loss that was more than twice as large as on any other single day from 1954 until 2004.exceedances;extreme value theory;heavy tails;maxima

The Meixner process : theory and applications in finance

The Meixner process is a special type of Levy process which origi-nates from the theory of orthogonal polynomials. It is related to the Meixner-Pollaczek polynomials by a martingale relation. We discuss sev-eral properties of the Meixner process. We apply the Meixner process to nancial data. First, we shows that the Normal distribution is a very poor model to t log-returns of nancial assets like stocks or indices. In order to achieve a better t we replace the Normal distribution by the more sophisticated Meixner distribution, taking into account, skewness and excess kurtosis. We show that the underlying Meixner distribution allows a much better t to the data by performing a number of statistical tests. Secondly, we introduce stock price models based on the Meixner process in order to price nancial derivatives. A rst signicant improvement can be achieved with respect to the famous Black-Scholes model (BS-model) by replacing its Brownian motion by the more exible Meixner process. However, there still is a discrepancy between market and theoretical prices. The main feature which these Levy models are missing is the fact that volatility or more generally the environment is changing stochastically over time. By making business time stochastic, an idea which was developed in [9], one can incorporate these stochastic volatility eects. The resulting option prices can be calibrated almost perfectly to empirical prices. 2

One-parameter extension of the Doi-Peliti formalism and relation with orthogonal polynomials

An extension of the Doi-Peliti formalism for stochastic chemical kinetics is proposed. Using the extension, path-integral expressions consistent with previous studies are obtained. In addition, the extended formalism is naturally connected to orthogonal polynomials. We show that two different orthogonal polynomials, i.e., Charlier polynomials and Hermite polynomials, can be used to express the Doi-Peliti formalism explicitly.Comment: 10 page

Conic coconuts : the pricing of contingent capital notes using conic finance

In this paper we introduce a fundamental model under which we will price contingent capital notes using conic finance techniques. The model is based on more realistic balance-sheet models recognizing the fact that asset and liabilities are both risky and have been treated differently taking into account bid and ask prices in a prudent fashion. The underlying theory makes use of the concept of acceptability and distorted expectations, which we briefly discuss. We overview some potential funded and unfunded contingent capital notes. We argue that the traditional core tier one ration is maybe not optimal, certainly when taking into account the presence of risky liabilities; we as an alternative introduce triggers based on capital shortfall. The pricing of 7 variations of funded as well as unfunded notes is overviewed. We further investigate the effect of the dilution factor and the grace factor. In an appendix we show conic balance sheets including contingent capital instruments

Model and calibration risks for the Heston model

Parameters of equity pricing models, such as the Heston's stochastic volatility model, have to be calibrated every day to new market data of European vanilla options by minimizing a particular functional. Hence, the optimal parameter set might turn out to vary significantly on a daily basis, depending on the quality of the initial guess and therefore on the local minima which is reached by the local optimizer method. However, thanks to the emergence of market data for volatility derivatives, practitioners might resort to time series or market quotes to determine some of the model parameters beforehand and perform therefore a calibration on a reduced parameter set. In particular, the spot variance v_0 of the Heston model can be inferred beforehand from the spot value of the volatility index whereas the long run variance \eta can be estimated either from the time series of the volatility index or from the VIX option surface. This paper provides a market-implied estimate of \eta which is inferred from the Put-Call parity for long maturity options on the VIX. We then compare the such obtained mark-to-market estimate with the \eta parameter obtained from the calibration and with the estimate inferred from the VIX time series by using either a moving window or the exponentially weighted moving average technique. Moreover, this paper features a detailed calibration performance study of the Heston model for the two calibration procedures, i.e. the standard calibration on the whole parameter set and the different reduced calibrations on the parameter set {\kappa, \lambda, \rho}. We also investigate the calibration risk which arises by considering different objective functions and/or different calibration methodologies and price a wide range of exotic options for the different calibration settings. For the numerical study, we consider daily S&P500 and VIX market quotes for a period extending from the 24th of February 2006 until the 31st of October 2009, including therefore the credit crunch