Modeling cause-of-death mortality using hierarchical Archimedean copula

Studying changes in cause-specific (or competing risks) mortality rates may provide significant insights for the insurance business as well as the pension systems, as they provide more information than the aggregate mortality data. However, the forecasting of cause-specific mortality rates requires new tools to capture the dependence among the competing causes. This paper introduces a class of hierarchical Archimedean copula (HAC) models for cause-specific mortality data. The approach extends the standard Archimedean copula models by allowing for asymmetric dependence among competing risks, while preserving closed-form expressions for mortality forecasts. Moreover, the HAC model allows for a convenient analysis of the impact of hypothetical reduction, or elimination, of mortality of one or more causes on the life expectancy. Using US cohort mortality data, we analyze the historical mortality patterns of different causes of death, provide an explanation for the ‘failure’ of the War on Cancer, and evaluate the impact on life expectancy of hypothetical scenarios where cancer mortality is reduced or eliminated. We find that accounting for longevity improvement across cohorts can alter the results found in existing studies that are focused on one single cohort.     

Combining random forest and copula functions: A heuristic approach for selecting assets from a financial crisis perspective

In this paper we propose a heuristic strategy aimed at selecting and analysing a set of financial assets, focusing attention on their multivariate tail dependence structure. The selection, obtained through an algorithmic procedure based on data mining tools, assumes the existence of a reference asset we are specifically interested to. The procedure allows one to opt for two alternatives: to prefer those assets exhibiting either a minimum lower tail dependence or a maximum upper tail dependence. The former could be a recommendable opportunity in a financial crisis period. For the selected assets, the tail dependence coefficients are estimated by means of a proper multivariate copula function. Copyright © 2010 John Wiley & Sons, Ltd.     

Structural asset pricing theory with wavelets

We apply Fourier and wavelet decompositions to structural asset pricing models with time non-separable utility. Through simulations, we show how Fourier decompositions of the utility function, coupled with isolating certain frequencies of the stochastic consumption process, reveal a preference for temporal allocations. We demonstrate the usefulness of wavelets by highlighting their ability to isolate frequency and time, simultaneously. While much work has been devoted to wavelet applications of financial data, we are unaware of papers that use wavelets to analyze structural aspects of asset pricing models.     

Asset pricing under information with stochastic volatility

Based on a general specification of the asset specific pricing kernel, we develop a pricing model using an information process with stochastic volatility. We derive analytical asset and option pricing formulas. The asset prices in this rational expectations model exhibit crash-like, strong downward movements. The resulting option pricing formula is consistent with the strong negative skewness and high levels of kurtosis observed in empirical studies. Furthermore, we determine credit spreads in a simple structural model.      

Asian option pricing with orthogonal polynomials

In this paper we derive a series expansion for the price of a continuously sampled arithmetic Asian option in the Black–Scholes setting. The expansion is based on polynomials that are orthogonal with respect to the log-normal distribution. All terms in the series are fully explicit and no numerical integration nor any special functions are involved. We provide sufficient conditions to guarantee convergence of the series. The moment indeterminacy of the log-normal distribution introduces an asymptotic bias in the series, however we show numerically that the bias can safely be ignored in practice.     

Testing market efficiency with the pricing kernel

Market efficiency and the pricing kernel are closely related. A non-monotonic decreasing pricing kernel implies the existence of a trading strategy in contingent claims that stochastically dominates a direct investment in the market. Moreover, a market is assumed to be efficient only if no dominating strategies exist. Empirically, many studies of the pricing kernel find non-monotonicity, apparently ruling out market efficiency. However, these results are often unreliable, because the pricing measures of the pricing kernel are estimated using differing filtration sets. We show this effect both theoretically and empirically, and we discuss recent approaches in the literature for achieving more reliable estimates of the pricing kernel, potentially leading to better tests of market efficiency.     

An Investigation of the Flight-to-Quality Effect: Evidence from Asia-Pacific Countries

Flight to quality has long been a feature of international financial markets when there are extreme variations in the negative relationship between returns on stocks and sovereign bond indices. This study analyzes the existence of a flight-to-quality effect from stocks to long-term government bonds in five Asia-Pacific countries by modeling a dependency structure from a copula-based perspective. The authors employ various copula functions to examine the degrees of dependence on symmetric and asymmetric structures in these countries. They find a negative relationship between stock and bond returns, that there is a flight to quality in the Asia-Pacific region, and that it intensified during the financial crisis period, indicating that investors considered government bonds to be safer financial instruments than stocks during this period. Furthermore, the authors show that the level of economic freedom in a country affects the tendency toward flight to quality.     

Market competitiveness and Big 5 pricing: Evidence from China's binary market

Big 5 auditors enjoy a worldwide audit fee premium that is believed to be attributable primarily to their reputation for providing high-quality services to clients. This study finds that the fee premium is also attributable to a lack of competition in the market. Taking advantage of the binary structure of the audit market in China, we compare the pricing practices of the Big 5 in the competitive statutory market and the less competitive supplementary market. Although the Big 5 have a reputation for high-quality audits in both markets, the degree of competition in the two markets is very different. Using audit fee data from the period 2000 to 2003, we find that the Big 5 earn a significant fee premium in the less competitive supplementary market, but not in the competitive statutory market. Although our results do not completely rule out reputation as an explanation, they are consistent with the notion that the audit fee premium that is earned by the Big 5 is more likely to be attributable to their dominant market position than to their reputation in the emerging Chinese markets, in which the usual audit-quality benefits for investors and managers are either absent or minimal.     

Realizing smiles: Options pricing with realized volatility

We develop a discrete-time stochastic volatility option pricing model exploiting the information contained in the Realized Volatility (RV), which is used as a proxy of the unobservable log-return volatility. We model the RV dynamics by a simple and effective long-memory process, whose parameters can be easily estimated using historical data. Assuming an exponentially affine stochastic discount factor, we obtain a fully analytic change of measure. An empirical analysis of Standard and Poor's 500 index options illustrates that our model outperforms competing time-varying and stochastic volatility option pricing models.     

Option pricing for GARCH-type models with generalized hyperbolic innovations

In this paper, we provide a new dynamic asset pricing model for plain vanilla options and we discuss its ability to produce minimum mispricing errors on equity option books. Given the historical measure, the dynamics of assets being modeled by Garch-type models with generalized hyperbolic innovations and the pricing kernel is an exponential affine function of the state variables, we show that the risk-neutral distribution is unique and again implies a generalized hyperbolic dynamics with changed parameters. We provide an empirical test for our pricing methodology on two data sets of options, respectively written on the French CAC 40 and the American SP 500. Then, using our theoretical result associated with Monte Carlo simulations, we compare this approach with natural competitors in order to test its efficiency. More generally, our empirical investigations analyse the ability of specific parametric innovations to reproduce market prices in the context of an exponential affine specification of the stochastic discount factor.     

Jump-Dependent Model for Optimal Index Futures Hedging in Five Major Asian Stock Markets

This article develops a jump-dependent model to capture the dependences between spot and futures returns and their jumps simultaneously, named JD model. We examine hedging performance of the presenting JD model for the futures contracts of Hong Kong, Japan, Korea, Singapore, and Taiwan. The results have shown that the JD model has better out-of-sample performance than the OLS for Korea, Singapore, and Taiwan. Since these three markets have higher jump dependence between spot and futures, we consider that jump dependence plays an important role in hedging performance. The higher jump dependence means spot and futures markets move more closely when unusual news reveals itself and thus futures could hedge the spot more effectively when extreme unusual news arrives.     

General equilibrium pricing with multiple dividend streams and regime switching

In this paper, we investigate a regime switching Lucas economy in continuous time, with multiple dividend streams and labour income. We determine the asset prices in equilibrium in the economy with regime switching, and derive a system of partial differential equations for the asset prices and the short interest rate. The solutions for the endogenous short interest rate, the bond price and the yield of the bond are obtained. We also consider applications of the equilibrium model and show that the model implies a rich framework for the term structure of interest rates. We demonstrate how the regime switching economy helps to improve the model-implied annual excess rate of return. This assists in explaining the famous equity premium puzzle.     

Bond pricing when the short-term interest rate follows a threshold process

This paper derives analytical solutions for arbitrage-free bond yields when the short-term interest rate follows an autoregressive process with the intercept switching endogenously. This process from the SETAR family is especially suited to capture the near-unit-root behaviour typically observed in the evolution of short-term interest rates. The derived yield functions, mapping the one-month rate into n-period yields, exhibit a convex/concave shape to the left and right of the threshold value, respectively, a pattern which is also found in US bond yield data. The longer the time to maturity, the more distinct the nonlinearity of the yield function becomes.     

Stochastic duration and fast coupon bond option pricing in multi-factor models

Generalizing Cox, Ingersoll, and Ross (1979), this paper defines the stochastic duration of a bond in a general multi-factor diffusion model as the time to maturity of the zero-coupon bond with the same relative volatility as the bond. Important general properties of the stochastic duration measure are derived analytically, and the stochastic duration is studied in detail in various well-known models. It is also demonstrated by analytical arguments and numerical examples that the price of a European option on a coupon bond (and, hence, of a European swaption) can be approximated very accurately by a multiple of the price of a European option on a zero-coupon bond with a time to maturity equal to the stochastic duration of the coupon bond. This revised version was published online in June 2006 with corrections to the Cover Date.     

Basket CDS pricing with interacting intensities

We propose a factor contagion model for correlated defaults. The model covers the heterogeneous conditionally independent portfolio and the infectious default portfolio as special cases. The model assumes that the hazard rate processes are driven by external common factors as well as defaults of other names in the portfolio. The total hazard construction method is used to derive the joint distribution of default times. The basket CDS rates can be computed analytically for homogeneous contagion portfolios and recursively for general factor contagion portfolios. We extend the results to include the interacting counterparty risk and the stochastic intensity process. The authors thank two anonymous referees for several suggestions which have helped to improve the earlier versions. The authors thank Sheng Miao for help in implementation with C++, Huiqi Pan for help in implementation with Fortran, and Xiaozhou Cao for help in implementation with MAPLE. Harry Zheng thanks the London Mathematical Society for its collaborative grant support (Grant 4544 and Grant 4707).     

Option pricing with random volatilities in complete markets

This article presents the theory of option pricing with random volatilities in complete markets. As such, it makes two contributions. First, the newly developed martingale measure technique is used to synthesize results dating from Merton (1973) through Eisenberg, (1985, 1987). This synthesis illustrates how Merton's formula, the CEV formula, and the Black-Scholes formula are special cases of the random volatility model derived herein. The impossibility of obtaining a self-financing trading strategy to duplicate an option in incomplete markets is demonstrated. This omission is important because option pricing models are often used for risk management, which requires the construction of synthetic options.Second, we derive a new formula, which is easy to interpret and easy to program, for pricing options given a random volatility. This formula (for a European call option) is seen to be a weighted average of Black-Scholes values, and is consistent with recent empirical studies finding evidence of mean-reversion in volatilities.Helpful comments from an anonymous referee are greatly appreciated.     

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.