A general class of distortion operators for pricing contingent claims with applications to CAT bonds

ABSTRACT

The current paper provides a general approach to construct distortion operators that can price financial and insurance risks. Our approach generalizes the (Wang 2000) transform and recovers multiple distortions proposed in the literature as particular cases. This approach enables designing distortions that are consistent with various pricing principles used in finance and insurance such as no-arbitrage models, equilibrium models and actuarial premium calculation principles. Such distortions allow for the incorporation of risk-aversion, distribution features (e.g. skewness and kurtosis) and other considerations that are relevant to price contingent claims. The pricing performance of multiple distortions obtained through our approach is assessed on CAT bonds data. The current paper is the first to provide evidence that jump-diffusion models are appropriate for CAT bonds pricing, and that natural disaster aversion impacts empirical prices. A simpler distortion based on a distribution mixture is finally proposed for CAT bonds pricing to facilitate the implementation.     

The Performance of Hedge Fund Strategies and the Asymmetry of Return Distributions

We present hedge fund performance estimates that adjust for stale prices, Fama‐French risk factors and skewness. We contrast these new performance estimates with traditional performance measures. Using three‐factor models to adjust for staleness in prices and to incorporate Fama‐French factors along with the Harvey‐Siddique (2000) two‐factor model that incorporates skewness, we find that for the period 1990–2003, all hedge fund categories achieve above average performance when measured against an aggregate market index. More significantly, however, when we estimate performance at the individual hedge fund level, we discover that only 40 to 47% of the funds are shown to achieve an above average performance over that time period depending on the model used. These results have important implications for investors, endowments and pensions when they choose hedge fund managers.     

A Bayesian Generalized Linear Model for the Bornhuetter-Ferguson Method of Claims Reserving

Abstract

This paper shows how Bayesian models within the framework of generalized linear models can be applied to claims reserving. The author demonstrates that this approach is closely related to the Bornhuetter-Ferguson technique. Benktander (1976) and Mack (2000) previously studied the Bornhuetter-Ferguson technique and advocated using credibility models. The present paper uses a Bayesian parametric model within the framework of generalized linear models.     

Bayesian comparison of several continuous time models of the Australian short rate

This paper provides an empirical analysis of a range of alternative single‐factor continuous time models for the Australian short‐term interest rate. The models are nested in a general single‐factor diffusion process for the short rate, with each alternative model indexed by the level effect parameter for the volatility. The inferential approach adopted is Bayesian, with estimation of the models proceeding through a Markov chain Monte Carlo simulation scheme. Discrimination between the alternative models is based on Bayes factors. A data augmentation approach is used to improve the accuracy of the discrete time approximation of the continuous time models. An empirical investigation is conducted using weekly observations on the Australian 90 day interest rate from January 1990 to July 2000. The Bayes factors indicate that the square root diffusion model has the highest posterior probability of all models considered.     

Why not use SDF rather than beta models in performance measurement?

This paper analyzes performance measurement based on stochastic discount factors, compared to beta models traditionally used in computing funds’ (Jensen) alphas. From a theoretical point of view, standard alphas suffer from several limitations. Our paper addresses this issue from an empirical point of view using a sample of Swiss mutual funds from 2000 to 2011. Our results suggest that the key for a “fair” comparison between stochastic discount function (SDF) and beta models is the specification of the set of primitive assets used to calibrate the SDF function. Once this is established, the size of (absolute) performance differences considerably decreases between the two model families. However, there are sizeable performance deviations in the cross-section of funds if conditioning information is incorporated in the tests, up to some 20 basis points per month, or about 2.3 % per year. In almost all cases, the SDF-alphas are lower than the standard (Jensen) alphas. In absolute terms, the average SDF-based underperformance of the funds is way larger than the average total expense ratio (TER) of the funds, both in a conditional and unconditional setting.     

Structural models of corporate bond pricing with personal taxes

The structural approach offers an integrated framework to deal with yield spreads and default probability simultaneously. However, structural models perform poorly in predicting corporate bond spreads. It is unclear whether this poor performance is caused by characteristics of individual models, missing factors, or different calibration procedures. This study evaluates the performance of four structural models by incorporating two important factors, personal taxes and the liquidity factor, and calibrating these models to data. To ensure our results are not contingent on the calibration method, we further apply the maximum likelihood estimation method to a large sample of individual bonds. Results consistently show that the ability of structural models to predict spreads improves considerably when personal taxes and liquidity are taken into account. Our findings suggest that the poor performance of standard structural models is more likely due to missing factors than the characteristics of individual models or the calibration procedure.     

An Empirical Examination of U.K. International Unit Trust Performance

We examine the performance of U.K. unit trusts with international equity objectives between January 1985 and December 2000 using four international factor models. The international version of the Carhart (1997) model performs the best in explaining the cross-section of international stock returns. There is little evidence of superior performance by international trusts relative to the global models. We also find that the choice between a local and global version of the Carhart model has a significant impact on the relation between the investment sector of the trust and performance.JEL classification: G10, G12     

Relative accuracy and predictive ability of direct valuation methods, price to aggregate earnings method and a hybrid approach

In this paper, we assess the relative performance of the direct valuation method and industry multiplier models using 41 435 firm‐quarter Value Line observations over an 11 year (1990–2000) period. Results from both pricing‐error and return‐prediction analyses indicate that direct valuation yields lower percentage pricing errors and greater return prediction ability than the forward price to aggregated forecasted earnings multiplier model. However, a simple hybrid combination of these two methods leads to more accurate intrinsic value estimates, compared to either method used in isolation. It would appear that fundamental analysis could benefit from using one approach as a check on the other.     

Measuring changes in credit risk: The case of CDS event studies

This paper examines the size and power of test statistics designed to detect abnormal changes in credit risk as measured by credit default swap (CDS) spreads. We follow a simulation approach to examine the statistical properties of normal and abnormal CDS spread changes and assess the performance of normal return models and test statistics. Using daily CDS data, we find parametric test statistics to be generally inferior to non-parametric tests, with the rank test performing best. A CDS factor model based on factors identified in the empirical literature is generally well specified and more powerful in detecting abnormal performance than some of the classical normal return models. Finally, we examine abnormal CDS announcement spread changes around issuer's rating downgrades to demonstrate the effect of different CDS spread change measures and normal return models on event study results.     

Option pricing under non-normality: a comparative analysis

This paper carries out a comparative analysis of the calibration and performance of a variety of options pricing models. These include Black and Scholes (J Polit Econ 81:637–659, 1973), the Gram–Charlier (GC) approach of Backus et al. (1997), the stochastic volatility (HS) model of Heston (Rev Financ Stud 6:327–343, 1993), the closed-form GARCH process of Heston and Nandi (Rev Financ Stud 13:585–625, 2000) and a variety of Lévy processes including the Variance Gamma (VG), Normal Inverse Gaussian (NIG), and, CGMY and Kou (Manag Sci 48:1086–1101, 2002) jump-diffusion models. Unlike most studies of option pricing, we compare these models using a common point-in-time data which reflects the perspective of a new investor who wishes to choose between models using only the most minimal recent data set. For each of these models, we also examine the accuracy of delta and delta-gamma approximations to the valuation of both individual options and an illustrative option portfolio.     

Portfolio allocation using multivariate variance gamma models

In this paper, we investigate empirically the effect of using higher moments in portfolio allocation when parametric and nonparametric models are used. The nonparametric model considered in this paper is the sample approach; the parametric model is constructed assuming multivariate variance gamma (MVG) joint distribution for asset returns.We consider the MVG models proposed by Madan and Seneta (1990), Semeraro (2008) and Wang (2009). We perform an out-of-sample analysis comparing the optimal portfolios obtained using the MVG models and the sample approach. Our portfolio is composed of 18 assets selected from the S&P500 Index and the dataset consists of daily returns observed from 01/04/2000 to 01/09/2011.     

Art of conversation as an antidote to cultural exclusion

Over recent years it has become apparent that students on the Business Studies and Leisure degree programmes at the University of Glamorgan perform poorly in the core accounting modules. Given that a high proportion of undergraduate accounting courses in the UK are delivered to nonspecialists, research into the performance of such students is important. With reference to previous literature, this study investigates the extent to which background factors affect the performance of students studying the nonspecialist Level 1 and Level 2 modules. The study is based on the September 1998 intake of students utilizing background information collected from the student files and performance measures from the university's Student Administration System. Explanatory variables are analysed using a factor analytical approach via principal component analysis. Multiple regression analysis is then performed on the results of the three accounting modules. The findings of this study are that the explanatory power of such models is limited and that perhaps a more qualitative approach to assessing factors influencing student performance would be more worthwhile.     

Identifying Term Structure Volatility from the LIBOR-Swap Curve

This paper proposes a new family of specification tests andapplies them to affine term structure models of the London InterbankOffered Rate (LIBOR)-swap curve. Contrary to Dai and Singleton(2000), the tests show that when standard estimation techniquesare used, affine models do a poor job of forecasting volatilityat the short end of the term structure. Improving the volatilityforecast does not require different models; rather, it requiresa different estimation technique. The paper distinguishes betweentwo econometric procedures for identifying volatility. The "cross-sectional"approach backs out volatility from a cross section of bond yields,and the "time-series" approach imputes volatility from time-seriesvariation in yields. For an affine model, the volatility impliedby the time-series procedure passes the specification tests,while the cross-sectionally identified volatility does not.This is surprising, since under correct specification, the "cross-sectional"approach is maximum likelihood. One explanation is that affinemodels are slightly misspecified; another is that bond yieldsdo not span volatility, as in Collin-Dufresne and Goldstein(2002).     

Australian retail fund performance persistence

The present study extends the Australian fund performance persistence literature through the use of five performance metrics: raw returns, the Sharpe ratio, the single‐factor model and two multifactor models, the Carhart (1997) model and the Gruber (1996) model, in analysis of Australian retail fund performance over the period 1991–2000. Analysis suggests that performance persistence is sensitive to fund objective and appears to be driven by inadequate adjustment for risk.     

The Great Inflation of the 1970s

The two leading explanations for the poor inflation performance during the 1970s are policy opportunism ( Barro and Gordon 1983 ) and "inadvertently" bad monetary policy ( Clarida, Gali, and Gertler 2000 , Orphanides 2003 ). The main models of the latter category are that of Orphanides (loose monetary policy was the outcome of mis-perceptions about potential output rather than of inflation tolerance) and of Clarida, Gali, and Gertler (weak policy reaction to expected inflation led to indeterminacies). We show that both of these models can account for high and persistent inflation and also have satisfactory overall performance if an exceptionally large decrease in productivity took place at that time.     

Fueling the buyout machine: fundraising in private equity

This paper analyzes the impact of performance, investment-firm-related, and macroeconomic variables on fundraising activities in private equity (PE). We use a novel, backward-looking approach to link current to preceding funds, which allows for including several parallel predecessor funds in our analysis. We employ logit and tobit models to a global sample of 1463 fundraising events observed between 2000 and 2010 in order to estimate the probability of raising and the volume of follow-on funds. Our results show that the average buyout duration of past transactions has a negative impact, whereas exits via an initial public offering (IPO) and deals without industry-style drift positively affect fundraising activities. Larger, industry-diversified, and independent PE firms exhibit a higher likelihood of fundraising and collect larger amounts.     

Intraday risk management in International stock markets: A conditional EVT approach

The study compares the predictive ability of various models in estimating intraday Value-at-Risk (VaR) and Expected Shortfall (ES) using high frequency share price index data from sixteen different countries across the world for a period of seven and half months from September 20, 2013 to May 07, 2014. The main emphasis of the study has been given to Extreme Value Theory (EVT) and to evaluate how well Conditional EVT model performs in modeling tails of distributions and in estimating and forecasting intraday VaR and ES measures. We have followed McNeil and Frey's (2000) two stage approach called Conditional EVT to estimate dynamic intraday VaR and ES. We have compared the accuracy of Conditional EVT approach to intraday VaR and ES estimation with other competing models. The best performing model is found to be the Conditional EVT in estimating both the quantiles for the entire sample. The study is useful for market participants (such as intraday traders and market makers) involved in frequent intraday trading in such equity markets.     

Realizing the extremes: Estimation of tail-risk measures from a high-frequency perspective

This article applies realized volatility forecasting to Extreme Value Theory (EVT). We propose a two-step approach where returns are first pre-whitened with a high-frequency based volatility model, and then an EVT based model is fitted to the tails of the standardized residuals. This realized EVT approach is compared to the conditional EVT of McNeil & Frey (2000). We assess both approaches' ability to filter the dependence in the extremes and to produce stable out-of-sample VaR and ES estimates for one-day and ten-day time horizons. The main finding is that GARCH-type models perform well in filtering the dependence, while the realized EVT approach seems preferable in forecasting, especially at longer time horizons.     

A Nonlinear Factor Analysis of S&P 500 Index Option Returns

Growing evidence suggests that extraordinary average returns may be obtained by trading equity index options, and that at least part of this abnormal performance is attributable to volatility and jump risk premia. This paper asks whether such priced risk factors are alone sufficient to explain these average returns. To provide an answer in as general as possible a setting, I estimate a flexible class of nonlinear models using all S&P 500 Index futures options traded between 1986 and 2000. The results show that priced factors contribute to these expected returns but are insufficient to explain their magnitudes, particularly for short‐term out‐of‐the‐money puts.