A profit model for spread trading with an application to energy futures

This paper proposes a profit model for spread trading by focusing on the stochastic movement of the price spread and its first hitting time probability density. The model is general in that it can be used for any financial instrument. The advantage of the model is that the profit from the trades can be easily calculated if the first hitting time probability density of the stochastic process is given. We then modify the profit model for a particular market, the energy futures market. It is shown that energy futures spreads are modeled by using a meanreverting process. Since the first hitting time probability density of a mean-reverting process is approximately known, the profit model for energy futures price spreads is given in a computable way by using the parameters of the process. Finally, we provide empirical evidence for spread trades of energy futures by employing historical prices of energy futures (WTI crude oil, heating oil, and natural gas futures) traded on the New York Mercantile Exchange. The results suggest that natural gas futures trading may be more profitable than WTI crude oil and heating oil due to its high volatility in addition to its long-term mean reversion, which offers supportive evidence of the model prediction. --futures spread trading,energy futures markets,mean-reverting process,first hitting,time probability density,profit model,WTI crude oil,heating oil,natural gas

CVaR sensitivity with respect to tail thickness

We consider the sensitivity of conditional value-at-risk (CVaR) with respect to the tail index assuming regularly varying tails and exponential and faster-than-exponential tail decay for the return distribution. We compare it to the CVaR sensitivity with respect to the scale parameter for stable Paretian, the Student's t, and generalized Gaussian laws and discuss implications for the modeling of daily returns and marginal rebalancing decisions. Finally, we explore empirically the impact on the asymptotic variability of the CVaR estimator with daily returns which is a standard choice for the return frequency for risk estimation. --fat-tailed distributions,regularly varying tails,conditional value-at-risk,marginal rebalancing,asymptotic variability

Analysis of the intraday effects of economic releases on the currency market

Using four years of second-by-second executed trade data, we study the intraday effects of a representative group of scheduled economic releases on three exchange rates: EUR/$, JPY/$ and GBP/$. Using wavelets to analyze volatility behavior, we empirically show that intraday volatility clusters increase as we approach the time of the releases, and decay exponentially after the releases. Moreover, we compare our results with the results of a poll that we conducted of economists and traders. Finally, we propose a wavelet volatility estimator which is not only more efficient than a range estimator that is commonly used in empirical studies, but also captures the market dynamics as accurately as a range estimator. Our approach has practical value in high-frequency algorithmic trading, as well as electronic market making. --Foreign exchange,volatility estimation,economic release,wavelet,high frequency

Bayesian inference for hedge funds with stable distribution of returns

Recently, a body of academic literature has focused on the area of stable distributions and their application potential for improving our understanding of the risk of hedge funds. At the same time, research has sprung up that applies standard Bayesian methods to hedge fund evaluation. Little or no academic attention has been paid to the combination of these two topics. In this paper, we consider Bayesian inference for alpha-stable distributions with particular regard to hedge fund performance and risk assessment. After constructing Bayesian estimators for alpha-stable distributions in the context of an ARMA-GARCH time series model with stable innovations, we compare our risk evaluation and prediction results to the predictions of several competing conditional and unconditional models that are estimated in both the frequentist and Bayesian setting. We find that the conditional Bayesian model with stable innovations has superior risk prediction capabilities compared with other approaches and, in particular, produced better risk forecasts of the abnormally large losses that some hedge funds sustained in the months of September and October 2008. --

Fat-tailed models for risk estimation

In the post-crisis era, financial institutions seem to be more aware of the risks posed by extreme events. Even though there are attempts to adapt methodologies drawing from the vast academic literature on the topic, there is also skepticism that fat-tailed models are needed. In this paper, we address the common criticism and discuss three popular methods for extreme risk modeling based on full distribution modeling and and extreme value theory. --

Tempered stable and tempered infinitely divisible GARCH models

In this paper, we introduce a new GARCH model with an infinitely divisible distributed innovation, referred to as the rapidly decreasing tempered stable (RDTS) GARCH model. This model allows the description of some stylized empirical facts observed for stock and index returns, such as volatility clustering, the non-zero skewness and excess kurtosis for the residual distribution. Furthermore, we review the classical tempered stable (CTS) GARCH model, which has similar statistical properties. By considering a proper density transformation between infinitely divisible random variables, these GARCH models allow to find the risk-neutral price process, and hence they can be applied to option pricing. We propose algorithms to generate scenario based on GARCH models with CTS and RDTS innovation. To investigate the performance of these GARCH models, we report a parameters estimation for Dow Jones Industrial Average (DJIA) index and stocks included in this index, and furthermore to demonstrate their advantages, we calculate option prices based on these models. It should be noted that only historical data on the underlying asset and on the riskfree rate are taken into account to evaluate option prices. --tempered infinitely divisible distribution,tempered stable distribution,rapidly decreasing tempered stable distribution,GARCH model option pricing

Tempered infinitely divisible distributions and processes

In this paper, we construct the new class of tempered infinitely divisible (TID) distributions. Taking into account the tempered stable distribution class, as introduced by in the seminal work of Rosinsky , a modification of the tempering function allows one to obtain suitable properties. In particular, TID distributions may have exponential moments of any order and conserve all proper properties of the Rosinski setting. Furthermore, we prove that the modified tempered stable distribution is TID and give some further parametric example. --stable distributions,tempered stable distributions,tempered infinitely divisible distributions,modified tempered stable distributions

Dynamic simulation of large-scale power systems using a parallel schur-complement-based decomposition method

Power system dynamic simulations are crucial for the operation of electric power systems as they provide important information on the dynamic evolution of the system after an occurring disturbance. This paper proposes a robust, accurate and efficient parallel algorithm based on the Schur complement domain decomposition method. The algorithm provides numerical and computational acceleration of the procedure. Based on the shared-memory parallel programming model, a parallel implementation of the proposed algorithm is presented. The implementation is general, portable and scalable on inexpensive, shared-memory, multi-core machines. Two realistic test systems, a medium-scale and a large-scale, are used for performance evaluation of the proposed method