Kevin Fergusson

On the distributional characterization of daily log-returns of a world stock index

In this paper distributions are identified which suitably fit log‐returns of the world stock index when these are expressed in units of different currencies. By searching for a best fit in the class of symmetric generalized hyperbolic distributions the maximum likelihood estimates appear to cluster in the neighbourhood of those of the Student t distribution. This is confirmed at a high significance level under the likelihood ratio test. Finally, the paper derives the minimal market model, which explains the empirical findings as a consequence of the optimal market dynamics.

APPLICATION OF MAXIMUM LIKELIHOOD ESTIMATION TO STOCHASTIC SHORT RATE MODELS

The application of maximum likelihood estimation is not well studied for stochastic short rate models because of the cumbersome detail of this approach. We investigate the applicability of maximum likelihood estimation to stochastic short rate models. We restrict our consideration to three important short rate models, namely the Vasicek, Cox–Ingersoll–Ross (CIR) and 3/2 short rate models, each having a closed-form formula for the transition density function. The parameters of the three interest rate models are fitted to US cash rates and are found to be consistent with market assessments.

Asymptotics Of Bond Yields And Volatilities For Extended Vasicek Models Under The Real-World Measure

Vasiceks short rate model is a mean reverting model of the short rate which permits closed-form pricing formulae of zero coupon bonds and options on zero coupon bonds. This paper supplies proofs which are valid for any single factor mean reverting Gaussian short rate model having time-inhomogeneous parameters. The formulae are for the expected present value of payoffs under the real-world probability measure, known as actuarial pricing. Importantly, we give formulae for asymptotic levels of bond yields and volatilities for extended Vasicek models when suitable conditions are imposed on the model parameters.

Explicit Formulae For Parameters Of Stochastic Models Of A Discounted Equity Index Using Maximum Likelihood Estimation With Applications

A discounted equity index is computed as the ratio of an equity index to the accumulated savings account denominated in the same currency. In this way, discounting provides a natural way of separating the modeling of the short rate from the market price of risk component of the equity index. In this vein, we investigate the applicability of maximum likelihood estimation to stochastic models of a discounted equity index, providing explicit formulae for parameter estimates. We restrict our consideration to two important index models, namely the Black–Scholes model and the minimal market model of Platen, each having an explicit formula for the transition density function. Explicit formulae for estimates of the model parameters and their standard errors are derived and are used in fitting the two models to US data. Further, we demonstrate the effect of the model choice on the no-arbitrage assumption employed in risk neutral pricing.

Partitions into large unequal parts from a general sequence

An asymptotic estimate is obtained for the number of partitions of the positive integer n into unequal parts coming from a sequence u , with each part greater than m , under suitable conditions on the sequence u . The estimate holds uniformly with respect to integers m such that 0 ≤ m ≤ n 1−δ , as n → ∞, where δ is a given real number, such that 0