http://lists.repec.org/mailman/listinfo/nep-ore Operations Research 2009-11-21 Walter Frisch http://d.repec.org/n?u=RePEc:uts:rpaper:255&r=ore In this paper a simulation approach fordefaultable yield curves is developed within the Heath etal.(1992) framework. The default event is modelled using the Cox process where the stochastic intensity represents the credit spread. The forward credit spread volatility function is affected by the entire credit spread term structure. The paper provides the defaultable bond and credit default swap option price in a probability setting equipped with a sub?ltration structure. The Euler-Maruyama stochastic integral approximation and the Monte Carlo method are applied to develop a numerical algorithm for pricing. Finally, the Antithetic Variable technique is used to reduce the variance of credit default swap option prices. Carl Chiarella, Viviana Fanelli, Silvana Musti 2009-08-01 pricing; HJM model; Cox process; Monte Carlo method; CDS option http://d.repec.org/n?u=RePEc:boc:bocoec:725&r=ore Conditional quantile estimation is an essential ingredient in modern risk management. Although GARCH processes have proven highly successful in modeling financial data it is generally recognized that it would be useful to consider a broader class of processes capable of representing more flexibly both asymmetry and tail behavior of conditional returns distributions. In this paper, we study estimation of conditional quantiles for GARCH models using quantile regression. Quantile regression estimation of GARCH models is highly nonlinear; we propose a simple and effective two-step approach of quantile regression estimation for linear GARCH time series. In the first step, we employ a quan- tile autoregression sieve approximation for the GARCH model by combining information over different quantiles; second stage estimation for the GARCH model is then carried out based on the first stage minimum distance estimation of the scale process of the time series. Asymptotic properties of the sieve approximation, the minimum distance estimators, and the final quantile regression estimators employing generated regressors are studied. These results are of independent interest and have applications in other quantile regression settings. Monte Carlo and empirical application results indicate that the proposed estimation methods outperform some existing conditional quantile estimation methods. Zhijie Xiao, Roger Koenker 2009-03-13 Quantile Regression, GARCH, Value-at-Risk http://d.repec.org/n?u=RePEc:uts:rpaper:256&r=ore This paper considers the problem of pricing American options when the dynamics of the underlying are driven by both stochastic volatility following a square root process as used by Heston(1993), and by a Poisson jump process as introduced by Merton (1976). Probability arguments are invoked to find a representation of the solution in terms of expectations over the joint distribution of the underlying process. A combination of Fourier transform in the log stock price and Laplace transform in the volatility is then applied to find the transition probability density function of the underlying process. It turns out that the price is given by an integral dependent upon the early exercise surface, for which a corresponding integral equation is obtained. The solution generalises in an intuitive way the structure of the solution to the corresponding European option pricing problem in the case of a call option and constant interest rates obtained by Scott (1997). Gerald Cheang, Carl Chiarella, Andrew Ziogas 2009-08-01 American options; stochastic volatility; jump-diffusion processes; Volterra integral equations; free boundary problem; method of lines