International Journal of Theoretical and Applied Finance

A basket default swap (BDS) is a credit derivative with contingent payments that are triggered by a combination of default events of the reference entities. A forward-starting basket default swap (FBDS) is a BDS starting at a specified future time. Existing analytic or semi-analytic methods for pricing FBDS are time consuming due to the large number of possible default combinations before the BDS starts. This paper develops a fast approximation method for FBDS based on the conditional independence framework. The method converts the pricing of a FBDS to an equivalent BDS pricing problem and combines Monte Carlo simulation with an analytic approach to achieve an effective method. This hybrid method is a novel technique which can be viewed either as a means to accelerate the convergence of Monte Carlo simulation or as a way to estimate parameters in an analytic method that are difficult to compute directly. Numerical results demonstrate the accuracy and efficiency of the proposed hybrid method.

This paper studies the option pricing problem in a class of models in which dividend yields follow a time-homogeneous diffusion. Within this framework, we develop a new approach for valuing options based on the use of a regularized Fourier transform. We derive a pricing formula for European options which gives the option price in the form of an inverse Fourier transform and propose two methods for numerically implementing this formula. As an application of this pricing approach, we introduce the Ornstein-Uhlenbeck and the square-root dividend yield models in which we explicitly solve the pricing problem for European options. Finally we highlight the main effects of a stochastic dividend yield on option prices.

It has been empirically verified that the strength of dependence in stock markets usually rises with volatility. In this paper we exploit this stylized fact combined with local maximum likelihood estimation of copula models to analyze the dynamic joint behavior of series of financial log returns. Explanatory variables based on the estimated GARCH volatilities are considered as potential regressors for explaining the dynamics in the copula parameters. The proposed model can assess and discriminate how much of the strength of dependence is due just to the time-varying volatility. The final local-parametric estimates may be used to compute risk measures, to simulate portfolio behavior, and so on. We illustrate our methods using two American indexes. Results indicate that volatility does affect the strength of dependence. The in-sample Value-at-Risk based on the dynamic model outperforms those based on the empirical estimates.

We consider a slight perturbation of the Hull-White short rate model and the resulting modified forward rate equation. We identify the model coefficients by using the martingale property of the normalized bond price. The forward rate and the system parameters are then estimated by using the maximum likelihood method.

We propose a simple univariate model for the dynamics of spot electricity prices. The model is nonparametric in the sense that it is free from parametric model assumptions and flexible in capturing the dynamics of the data. The estimation is performed in two steps. Preliminarily, spikes are identified by means of an iterative filtering technique. The series of spikes is used to estimate a seasonal spike intensity function and fitted with an exponential law. We then implement Nadaraya-Watson estimators for the drift and the diffusion coefficients on the filtered series. Monte Carlo simulations are used to evaluate estimation errors.

We fit the model on European and American time series of spot day-ahead electricity prices; in spite of the simplicity of the proposed model, our specification tests indicate successful goodness-of-fit. We provide evidence for mean-reversion, nonlinear volatility and seasonal spike intensity; moreover we find that American markets show a very low level of mean reversion and a lower volatility with respect to their European counterparts.

In this paper we describe a recursive Bayesian algorithm for the estimation of forward price models. The forward price is modeled within the benchmark framework for a forward price volatility function which includes a stochastic variable; a forward price with a liquidly traded maturity. A relationship between the bond price, the spot price and certain forward prices is stated. We set up the stochastic real world dynamics for these discretely compounded market observed forward prices. We propose a dynamic Bayesian estimation algorithm for a Monte Carlo time-discretized version of the resulting forward prices dynamics. The parameter to be estimated is a vector consisting of the forward price volatility parameters and the benchmarked bond price volatility parameters.

This paper studies the probability distribution and option pricing for drawdown in a stochastic volatility environment. Their analytical approximation formulas are derived by the application of a singular perturbation method (Fouque et al., 2000). The mathematical validity of the approximation is also proven. Then, numerical examples show that the instantaneous correlation between the asset value and the volatility state crucially affects the probability distribution and option prices for drawdown.