Pricing equity linked annuities under regime switching generalized gamma process

We propose a model for valuing equity linked annuity (ELA) products under a generalized gamma model with a Markov-switching compensator. We suppose that the market interest rate and all the parameters of the underlying reference portfolio switch over time according to the state of an economy, which is modelled by a continuous-time Markov chain. The model considered here can provide market practitioners with flexibility in modelling the dynamics of the reference portfolio. We price the ELA by pricing its embedded options, for which we employ the regime-switching version of Esscher transform to determine the pricing kernel. A system of coupled partial-differential-integral equations satisfied by the embedded option prices is derived. Simulation results of the model have been presented and discussed

A new lifetime model with different types of failure rate

A new class of lifetime distributions, which can exhibit with upside-down bathtub-shaped, bathtub-shaped, decreasing, and increasing failure rates, is introduced. The new distribution is constructed by compounding generalized Weibull and logarithmic distributions, leading to improvement on the lifetime distribution considered in Dimitrakopoulou et al. (2007) by having no restriction on the shape parameter and extending the result studied by Tahmasbi and Rezaei (2008) in the general form. The proposed model includes the exponential-logarithmic and Weibull-logarithmic distributions as special cases. Various statistical properties of the proposed class are discussed. Furthermore, estimation via the maximum likelihood method and the Fisher information matrix are discussed. Applications to real data demonstrate that the new class of distributions is more flexible than other recently proposed classes

A non-parametric estimation for implied volatility

We provide a non-parametric method for stochastic volatility modelling. Our method allows the implied volatility to be governed by a general Levy-driven Ornstein{Uhlenbeck process, the density function of which is hidden to market participants. Using discrete-time observation we estimate the density function of the stochastic volatility process via developing a cumulant M-estimator for the Levy measure. In contrast to other non-parametric estimators (such as kernel estimators), our estimator is guaranteed to be of the correct type. We implement this method with the aid of a support-reduction algorithm, which is an ecient iterative unconstrained optimisation method. For the empirical analysis, we use discretely observed data from two implied volatility indices, VIX and VDAX. We also present an out-of-sample test to compare the performance of our method with other parametric models

Forecasting spikes in electricity return innovations

This paper evaluates the accuracy of several hundred one-day-ahead value at risk (VaR) forecasts for predicting Australian electricity returns. We propose a class of observation-driven time series models referred to as asymmetric exponential generalised autoregressive score (AEGAS) models. The mechanism to update the parameters over time is provided by the scaled score of the likelihood function in the AEGAS model. Based on this new approach, the results provide a unified and consistent framework for introducing time-varying parameters in a wide class of non-linear models. The Australian energy markets is known as one of the most volatile and, when compared to some well-known models in the recent literature as benchmarks the fitting and forecasting results demonstrate the superior performance and considerable flexibility of proposed model for electricity markets

Forecasting the joint distribution of Australian electricity prices using dynamic vine copulae

We consider the problem of modelling and forecasting the distribution of a vector of prices from interconnected electricity markets using a flexible class of drawable vine copula models, where we allow the dependence parameters of the constituting bivariate copulae to be time-varying. We undertake in-sample and out-of-sample tests using daily electricity prices, and evidence that our model provides accurate forecasts of the underlying distribution and outperforms a set of competing models in their abilities to forecast one-day-ahead conditional quantiles of a portfolio of electricity prices. Our study is conducted in the Australian National Electricity Market (NEM), which is the most efficient power auction in the world. Electricity prices exhibit highly stylised features such as extreme price spikes, price dependency between regional markets, correlation asymmetry and non-linear dependency. The developed approach can be used as a risk management tool in the electricity retail industry, which plays an integral role in the apparatus of modern energy markets. Electricity retailers are responsible for the efficient distribution of electricity, while being exposed to market risk with extreme magnitudes

Measuring systemic risk using vine-copula

We present an intuitive model of systemic risk to analyse the complex interdependencies between different borrowers. We characterise systemic risk by the way that financial institutions are interconnected. Using their probability of default, we classify different international financial institutions into five rating groups. Then we use the state-of-the-art canonical (C-) and D-vine copulae to investigate the partial correlation structure between the rating groups. Amongst many interesting findings, we discover that the second tier financial institutions pay a larger contribution to the systemic risk than the top tier borrowers. Further, we discuss an application of our methodology for pricing credit derivative swaps