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We propose a novel mortality improvement model with the difference of death counts follows the Skellam distribution. We extend Mitchell et al. (2013) by considering the difference in Poisson death counts instead of the ratio of subsequent mortality rate, which does not have a known distribution. We derive the iterative estimators of the model from the Skellam distribution. Our model can employ maximum likelihood estimation for estimation issues such as missing data and provides a better fit than Mitchell et al. (2013) . Using English and Wales mortality rate age 0-89 data during 1950-2016, the model estimate suggests that the age-dependent mortality improvement is slower than the benchmark, which coincides with a recent observation by Office for National Statistics (2018) . The forecasting performance outperforms the Poisson and M10 model. We make inferences on the price of longevity swaps and analyze how the volatility shock of mortality improvement affects the premium of longevity swaps.

We propose a new neighbouring prediction model for mortality forecasting. For each mortality rate at age x in year t, mx,t, we construct an image of neighbourhood mortality data around mx,t, that is, Ꜫmx,t (x1, x2, s), which includes mortality information for ages in [x-x1, x+x2], lagging k years (1 ≤ k ≤ s). Combined with the deep learning model – convolutional neural network, this framework is able to capture the intricate nonlinear structure in the mortality data: the neighbourhood effect, which can go beyond the directions of period, age, and cohort as in classic mortality models. By performing an extensive empirical analysis on all the 41 countries and regions in the Human Mortality Database, we find that the proposed models achieve superior forecasting performance. This framework can be further enhanced to capture the patterns and interactions between multiple populations.

This article models the dynamics of age-specific incremental mortality as a stochastic process in which the drift rate can be simply and effectively modeled as the average annual improvement rate of a group time trend for all ages and the distribution of residuals can be fitted by one of the Gaussian distribution and four non-Gaussian distributions (Student t, jump diffusion, variance gamma, and normal inverse Gaussian). We use the one-factor copula model with six distributions for the factors (normal–normal, normal–Student t, Student t–normal, Student t–Student t, skewed t–normal, and skewed t–Student t) to capture the inter-age mortality dependence. We then construct three annuity portfolios (Barbell, Ladder, and Bullet) with equal portfolio value (total net single premium) and portfolio mortality duration but different portfolio mortality convexities. Finally, we apply our model to managing longevity risk by an approximation to the change in the portfolio value in response to a proportional or constant change in the force of mortality, and by estimating Value at Risk for the three annuity portfolios.

Adverse weather-related risk is a main source of crop production loss and a big concern for agricultural insurers and reinsurers. In response, weather risk hedging may be valuable, however, due to basis risk it has been largely unsuccessful to date. This research proposes the Lévy subordinated hierarchical Archimedean copula model in modelling the spatial dependence of weather risk to reduce basis risk. The analysis shows that the Lévy subordinated hierarchical Archimedean copula model can improve the hedging performance through more accurate modelling of the dependence structure of weather risks and is more efficient in hedging extreme downside weather risk, compared to the benchmark copula models. Further, the results reveal that more effective hedging may be achieved as the spatial aggregation level increases. This research demonstrates that hedging weather risk is an important risk management method, and the approach outlined in this paper may be useful to insurers and reinsurers in the case of agriculture, as well as for other related risks in the property and casualty sector.

This paper provides an optimal asset allocation strategy to enhance risk management performance in the face of a financial crisis; this strategy entails constructing a good asset model – a multivariate jump-diffusion (MJD) model which includes idiosyncratic and systematic jumps simultaneously – and choosing suitable asset allocations and objective functions for fund management. This study also provides the dependence structure for the MJD model. The empirical implementation demonstrates that the proposed MJD model provides more detailed information about the financial crisis, allowing fund managers to determine an appropriate asset allocation strategy that enhances investment performance during the crisis.

Option pricing and managing equity linked insurance (ELI) require the proper modeling of stock return dynamics. Due to the long duration nature of equity-linked insurance products, a stock return model must be able to deal simultaneously with the preceding stylized facts and the impact of market structure changes. In response, this article proposes stock return dynamics that combine Levy processes in a regime-switching framework. We focus on a non-Gaussian, generalized hyperbolic distribution. We use the most popular linked equity of ELIs, the S&P 500 index, as an example. The empirical study verifies that the proposed regime-switching generalized hyperbolic (RSGH) model gives the best fit to data. In investigating the effects of stock return modeling on pricing and risk management for financial contracts, we derive the characteristic function, embedded option price, and risk measure of equity-linked insurance analytically. More importantly, we demonstrate that the regime-switching generalized hyperbolic ...

This article proposes a new copula model known as the Levy subordinated hierarchical Archimedean copulas (LSHAC) for multicountry mortality dependence modeling. To the best of our knowledge, this is the first article to apply the LSHAC model to mortality studies. Through an extensive empirical analysis on modeling mortality experiences of 13 countries, we demonstrate that the LSHAC model, which has the advantage of capturing the geographical structure of mortality data, yields better fit, compared to the elliptical copulas. In addition, the proposed LSHAC model generates out-of-sample forecasts with smaller standard deviations, when compared to other benchmark copula models. The LSHAC model also confirms that there is an association between geographical locations and dependence of the overall mortality improvement. These results yield new insights into future longevity risk management. Finally, the model is used to price a hypothetical survival index swap written on a weighted mortality index. The results highlight the importance of dependence modeling in managing longevity risk and reducing population basis risk.

Levy subordinated hierarchical Archimedean copulas (LSHAC) are flexible models in high dimensional modeling. However, there is limited literature discussing their applications, largely due to the challenges in estimating their structures and their parameters. In this paper, we propose a three-stage estimation procedure to determine the hierarchical structure and the parameters of a LSHAC. This is the first paper to empirically examine the modeling performances of LSHAC models using exchange traded funds. Simulation study demonstrates the reliability and robustness of the proposed estimation method in determining the optimal structure. Empirical analysis further shows that, compared to elliptical copulas, LSHACs have better fitting abilities as well as more accurate out-of-sample Value-at-Risk estimates with less parameters. In addition, from a financial risk management point of view, the LSHACs have the advantage of being very flexible in modeling the asymmetric tail dependence, providing more conservative estimations of the probabilities of extreme downward co-movements in the financial market.

The impact of systematic risk on volatility skew is assessed in a CAPM–GARCH framework under which the relationship between asset price and market index adheres to the CAPM with each residual following an asymmetric GARCH process. From numerical analysis, we demonstrate that (1) the relation between beta and implied volatilities presents a beta smile; (2) beta can determine the shape of implied volatility curve, but systematic risk proportion (SRP) cannot; and (3) the degree of negative skewness and positive kurtosis is proportional to the SRP; however, a higher SRP does not always lead to a higher level of implied volatility.

This paper introduces mortality dependence in multi-country mortality modeling using a dynamic copula approach. Specifically, we use time-varying copula models to capture the mortality dependence structure across countries, examining both symmetric and asymmetric dependence structures. In addition, to capture the phenomenon of a heavy tail for the multi-country mortality index, we consider not only the setting of Gaussian innovations but also non-Gaussian innovations under the Lee–Carter framework model. As tests of the goodness of fit of different dynamic copula models, the pattern of mortality dependence, and the distribution of the innovations, we used empirical mortality data from Finland, France, the Netherlands, and Sweden. To understand the effect of mortality dependence on longevity derivatives, we also built a valuation framework for pricing a survivor index swap, then investigated the fair swap rates of a survivor swap numerically. We demonstrate that failing to consider the dynamic copula mortality model and non-Gaussian innovations would lead to serious underestimations of the swap rates and loss reserves.

In this paper, we propose AR-GARCH (autoregression-generalized autoregressive conditional heteroskedasticity) models to fit and forecast mortality rates for a given age by two alternative approaches. Specifically, one approach is to fit a time series of mortality rates for some age to an AR( n )-GARCH(1, 1) model, and project the mortality rate for that age in the next n th year; the other is to fit an AR(1)-GARCH(1, 1) model, and project the mortality rates recursively for the age in the next consecutive years. Further, we employ the copula method to capture the inter-age mortality dependence. Adopting mortality data of Japan, the UK, and the USA, we demonstrate that it is indispensable to consider the conditional heteroskedasticity in our mortality models which provide better performances in out-of-sample projection and prediction intervals with a higher degree of coverage than the Lee–Carter model. Finally, we numerically illustrate with mortality data of Japan that VaR (Value at Risk) values for longevity risk, regarded as additional reserves for annuity or pension providers, will be overestimated if the conditional heteroskedasticity or/and the inter-age mortality dependence structure are ignored.

The Al–Ni–Y–X (X = Cu, Ta, Zr) thin film metallic glasses are manufactured by sputtering, and their optical reflectivity characteristics are explored. The relationship among composition, atomic structure and reflectivity performance is established. Compared with pure Al films, the Al–Ni–Y film surface roughness is much lower and hardness is much higher, more suitable for optical reflector applications. For composite Al–Ni–Y films, the reflectance varies within 80–91%. For fully amorphous films, the reflectivity exhibits unusual uniform reflection at ~ 70%, perfect for broad-band reflector.

This article presents a closed-form formula for calculating the loan-to-value (LTV) ratio in an adjusted-rate reverse mortgage (RM) with a lump sum payment. Previous literatures consider the pricing of RM in a constant interest rate assumption and price it on fixed-rate loans. This paper successfully considers the dynamic of interest rate and the adjustable-rate RM simultaneously. This paper also considers the housing price shock into the valuation model. Assuming that house prices follow a jump diffusion process with a stochastic interest rate and that the loan interest rate is adjusted instantaneously according to the short rate, we demonstrate that the LTV ratio is independent of the term structure of interest rates. This argument holds even when housing prices follow a general process: an exponential Levy process. In addition, the HECM (Home Equity Conversion Mortgage) program may be not sustainable, especially for a higher level of housing price volatility. Finally, when the loan interest rate is adj...

This article provides an iterative fitting algorithm to generate maximum likelihood estimates under the Cox regression model and employs nonGaussian distributions-the jump diffusion (JD), variance gamma (VG), and normal inverse Gaussian (NIG) distributions-to model the error terms of the Renshaw and Haberman (2006) (RH) model. In terms of mean absolute percentage error, the RH model with non-Gaussian innovations provides better mortality projections, using 1900-2009 mortality data from England and Wales, France, and Italy. Finally, the lower hedge costs of longevity swaps according to the RH model with non-Gaussian innovations are not only based on the lower swap curves implied by the best prediction model, but also in terms of the fatter tails of the unexpected losses it generates.IntroductionLongevity represents an increasingly important risk for defined benefit pension plans and annuity providers, because life expectancy is dramatically increasing in developed countries. In 2007, exposures to improved life expectancy amounted to $400 billion for pension funds and insurance companies in the United Kingdom and United States (see Loeys, Panigirtzoglou, and Ribeiro, 2007). Stochastic mortality models quantify mortality and longevity risks, which makes mortality risk management possible and provides the foundation for pricing and reserving. Among all stochastic mortality models, the Lee-Carter (LC) model, proposed in 1992, is one of the most popular choices because of its ease of implementation and acceptable prediction errors in empirical studies. Various modifications of the LC model have been extended by Brouhns, Denuit, and Vermunt (2002), Renshaw and Haberman (2003, 2006), Cairns, Blake, and Dowd (2006), Li and Chan (2007), Biffis, Denuit, and Devolder (2010), and Hainaut (2012) to attain a broader interpretation. Cairns, Blake, and Dowd (2006) propose a two-factor stochastic mortality model, the CBD model, in which a first factor affects mortality at all ages, whereas a second factor affects mortality at older ages much more than at younger ages. Modeling the number of deaths with the Poisson model, Cairns et al. (2009) classify and compare eight stochastic mortality models, including an extension of the CBD model, with mortality data from England and Wales and the United States. They find that an extension of the CBD model that incorporates the cohort effect fits the English and Welsh data best, whereas for the U.S. data, the Renshaw and Haberman (2006) (RH) model, which also allows for a cohort effect, provides the best fit (Cairns et al., 2009). In addition to the cohort effect, short-term catastrophic mortality events, such as the influenza pandemic in 1918 and the Tsunami in December 2004, may lead to much higher mortality rates. Using empirical data from 1900 to 1984, we find that the residuals in the RH model for England and Wales, France, and Italy exhibit leptokurticity. It is crucial to address such mortality jumps in age-period-cohort mortality models. The main goal of this study is to incorporate non-Gaussian innovations into the RH model.To take heavy-tailed distributions into account in stochastic mortality models, Milidonis, Lin, and Cox (2011) use a Markov regime-switching model to analyze the 1901-2005 U.S. population mortality data and price mortality securities. In contrast, Biffis (2005) employs affine jump diffusions to model asset prices and mortality dynamics and thus addresses the risk analysis and market valuation of life insurance contracts. For Italian mortality data, Luciano and Vigna (2005) demonstrate that a diffusion process with a jump component (JD) provides a better fit than does a diffusion component in stochastic mortality processes. Cox, Lin, and Wang (2006) employ the JD process to model age-adjusted mortality rates for the United States and United Kingdom and to evaluate the first pure mortality security: the Swiss Re Vita bond. In addition, Lin and Cox (2008) combine a Brownian motion and a discrete Markov chain with a log-normal jump size distribution to price mortality-based securities in an incomplete market framework. …

To offer a means for insurance companies to deal with longevity risk, this article investigates a natural hedging strategy and attempts to find an optimal allocation of insurance products. Unlike prior research, this proposed natural hedging model can account for both the variance and mispricing effects of longevity risk at the same time. In addition, this study employs experience mortality rates, obtained from life insurance companies, rather than population mortality data for life insurance and annuity products.

To deal with multi-country longevity risk, this article investigates the long-run equilibrium of mortality rates and introduces mortality correlations across countries as a means for pricing a multi-country longevity bond. The examination of the long-run equilibrium of the mortality rate relies on co-integration analysis, and a vector error correction model (VECM) is proposed for mortality forecasts. Mortality correlations among different countries under a VECM model are then derived. We take into account the mortality correlations across countries and utilize the multivariate Wang transform to derive the valuation formula for pricing the longevity bonds, with payoffs based on a combined weighted mortality index. This study illustrates the pattern of mortality correlations for men and women in the US and the UK, according to the Human Mortality Database. Our results show that mortality correlations across countries have a significant impact on pricing longevity bonds.

This article introduces cohort mortality dependence in mortality modeling. We extend the classical Lee-Carter model to incorporate cohort mortality dependence by considering mortality correlations for a cohort of people born in the same year. The pattern of cohort mortality dependence is demonstrated on the basis of U.S. mortality experience. We study the effect of cohort mortality dependence on the pricing of survivor derivatives. For this purpose, a survivor floor is introduced. To understand the difference between a survivor floor and other survivor securities, the valuation formulas for survivor swaps and survivor floors are all derived in detail and the effects of cohort mortality dependence on pricing survivor derivatives are investigated numerically. INTRODUCTION Longevity risk has become an increasingly important consideration for defined benefit pension plans and annuity providers, because life expectancy is increasing dramatically in developed countries. In 2007, exposure to improvements in life expectancy reached $400 billion for pension fund and insurance companies in the United Kingdom and United States (see Loeys, Panigirtzoglou, and Ribeiro, 2007). Therefore, finding a way to measure longevity risk and transferring the longevity risk away from the pension fund or annuity provider is of great interest to plan sponsors. Reinsurance, which represents a traditional means to transfer the longevity risk, can be expensive and involves a potential credit risk to the counterparty. In turn, many life insurance companies are less willing to buy reinsurance for their longevity risk. Instead, capital market solutions such as mortality-linked securities have emerged. Blake and Burrows (2001) were the first to advocate the use of mortality-linked securities to transfer longevity risk to capital markets. They suggested that the governments should help insurance companies hedge their mortality risks by issuing survivor bonds whose coupon payments depend on the proportion of the population surviving to particular ages. The longevity bond launched by the European Investment Bank (EIB) was the first securitization instrument designed to transfer longevity risk but ultimately was not issued and remained theoretical. Furthermore, various new securitization instruments and derivatives for longevity risk, such as survivor swaps, survivor futures, and survivor options, have received great attention among academics and practitioners (Blake, Cairns, and Dowd, 2006; Blake et al., 2010; Dowd et al., 2006; Biffs and Blake, 2009). The first derivative transaction, a q-forward contract, was issued in January 2008 between Lucida (1) and J.P. Morgan (Coughlan et al., 2007). In addition, the first survivor swap executed in the capital markets took place between Canada Life and a group of ILS and other investors in July 2008. In this context, the valuation of mortality-linked securities represents an important research topic for the development of capital market solutions for longevity risk. The dynamics of underlying mortality indexes have important effects on valuing life insurance or mortality-linked securities. The Lee-Carter model (Lee and Carter, 1992) has proved an effective method for mortality forecasts, which Denuit, Devolder, and Goderniaux (2007) use to value longevity bonds. Cairns, Blake, and Dowd (2006) also propose a two-factor stochastic mortality model (hereafter denoted CBD model) for higher ages and examine the pricing of longevity bonds. The Lee-Carter and CBD models both project mortality rates based on age and period effects. Renshaw and Haberman (2006) extend the Lee-Carter model to consider cohort effects (2) in mortality modeling. Cairns et al. (2009) quantitatively compare eight stochastic mortality models and demonstrate that the CBD model (Cairns, Blake, and Dowd, 2006) that incorporates a cohort effect fits data about English and Welsh men best, and Renshaw and Haberman's (2006) extension of the Lee-Carter model that also allows for a cohort effect provides the best fit for data pertaining to U. …

For the valuation of reverse mortgages with tenure payments, this article proposes a specific analytic valuation framework with mortality risk, interest rate risk, and housing price risk that helps determine fair premiums when the present value of premiums equals the present value of contingent losses. The analytic valuation of reverse mortgages with tenure payments is more complex than the valuation with a lump sum payment. This study therefore proposes a dimension reduction technique to achieve a closed-form solution for reverse annuity mortgage insurance, conditional on the evolution of interest rates. The technique provides strong accuracy, offering important implications for lenders and insurers.

Numerous empirical studies, including Abraham and Hendershott (1996), Muellbauer and Murphy (1997), Leung (2004), and Oikarinen (2009), have identified a significant relationship between housing prices and macroeconomic factors. Using a linear regression on the comovement of macroeconomic factors and housing prices, this article employs an option-pricing framework to price and hedge the fair premia of mortgage insurance (MI). Our model provides improved performance in terms of MI premium pricing, especially during periods that are characterized by high housing prices. Ignoring the impacts of macroeconomic factors on housing prices will lead to an underestimation of MI premia.

When the outstanding balance exceeds the housing value before the loan is settled, the insurer suffers an exposure to crossover risk induced by three risk factors: interest rates, house prices and mortality rates. With consideration of housing price risk, interest rate risk and longevity risk, we provide a three-dimensional lattice method that simultaneously captures the evolution of housing prices and short-term interest rates to calculate the fair valuation of reverse mortgages numerically. For a reverse mortgage insurer, the premium structure of reverse mortgage insurance is determined by setting the present value of the total expected claim losses equal to the present value of the premium charges. However, when the actual loss is higher than the expected loss, the insurer will incur an unexpected loss. To offset the potential loss, we also design two types of crossover bonds to transfer the unexpected loss to bond investors. Therefore, through the crossover bonds, reverse mortgage insurers can partially transfer crossover risk onto bond holders.

This paper proposes four methods by which to sample option prices using proxies for liquidity—1-, 2-, 3-, 7-, and 8-day rollover rules—for option trades in order to construct volatility index series. Based on the sampling method using the average of all midpoints of bid and ask quote option prices, the volatility indices constructed by one-minute tick data have less missing data and are at least as efficient in volatility forecasting as the method suggested by the CBOE. In addition, based on different rollover rules, illiquidity in Taiwan's options market does not lead to substantial errors in the forecasting effectiveness of the volatility indices. Finally, the forecasting ability of VIX based on different sampling methods is found to be superior to that of VXO in Taiwan.

Under a no-arbitrage assumption, the futures price converges to the spot price at the maturity of the futures contract, where the basis equals zero. Assuming that the basis process follows a modified Brownian bridge process with a zero basis at maturity, we derive the closed-form solutions of futures and futures options with the basis risk under the stochastic interest rate. We make a comparison of the Black model under a stochastic interest rate and our model in an empirical test using the daily data of S&P 500 futures call options. The overall mean errors in terms of index points and percentage are −4.771 and −27.83%, respectively, for the Black model and 0.757 and 1.30%, respectively, for our model. This evidence supports the occurrence of basis risk in S&P 500 futures call options.

In the classical Lee-Carter model, the mortality indices that are assumed to be a random walk model with drift are normally distributed. However, for the long-term mortality data, the error terms of the Lee-Carter model and the mortality indices have tails thicker than those of a normal distribution and appear to be skewed. This study therefore adopts five non-Gaussian distributions—Student’s t-distribution and its skew extension (i.e., generalised hyperbolic skew Student’s t-distribution), one finite-activity Levy model (jump diffusion distribution), and two infinite-activity or pure jump models (variance gamma and normal inverse Gaussian)—to model the error terms of the Lee-Carter model. With mortality data from six countries over the period 1900–2007, both in-sample model selection criteria (e.g., Bayesian information criterion, Kolmogorov–Smirnov test, Anderson–Darling test, Cramer–von-Mises test) and out-of-sample projection errors indicate a preference for modelling the Lee-Carter model with non-Gaussian innovations.

With the intersection of market and credit risk, the first contribution is to derive the analytic formulas of the Credit Linked Notes (CLNs) and the leveraged total return CLNs issued by an Special Purpose Vehicle (SPV) or the protection buyer. The second contribution is to prove that the values of structured CLNs issued by an SPV are higher than the ones issued by the protection buyer. When the credit quality of the reference obligation and protection buyer becomes worse or the leverage effect is higher, it is a superior solution for the structured CLNs issued through an SPV. Third, the empirical results of credit spreads do not incorporate the correlation coefficient of spot rate and market index into their regression models and show that they are positively correlated with the volatilities of spot rate and return on market index; however, we find that the relationship among them depends on the sign of correlation coefficient of spot rate and equity index market. Finally, using the differences in the ma...

This study empirically tests the performance of the Future Option model with Basis Risk (FOBR) proposed by Wang et al. (2005). The Black (1976) model is used as the competing model in this empirical test. The basis risk is the only difference between the two competing models and is therefore used to determine the existence of basis risk. The FOBR model is empirically tested using the daily data of S&P 500 call options on futures. The model outperforms Black's model due to its better prediction power. For the total sample data, the mean errors in terms of index and percentages are 0.973 and 1.0% for the FOBR model, and they are −4.468 and −27.1% for Black's model. The empirical test also supports the occurrence of basis risk in futures options on stock index by eliminating systematic moneyness and time-to-maturity biases produced by Black's model.

The article makes two contributions to the literature. The first contribution is to derive a closed-form solution of Taiwanese capped options. We also provide the properties of Taiwanese capped options and the phenomenon of delta jump at monitoring dates. When the interest rate changes dramatically, instead of deriving the pricing formulas for derivatives separately, the second contribution is to provide the closed-form solution of generalized capped exchange options with stochastic barriers under the Hull and White framework. Special cases of generalized capped exchange options with stochastic barriers are abundant. They include capped (floored) options, capped (floored) options with exponential barriers, capped (floored) options with related assets or indices as triggers and capped (floored) options with related assets or indices as triggers and other related assets as barriers.

Assuming that a futures price is a function of the underlying asset and the basis, and that a Brownian bridge process drives the basis, this article provides the closed-form solution of futures with basis risk (FBR). The Brownian bridge process ensures that the basis is zero at the maturity of a futures contract. The FBR model is empirically tested with daily S&P500 futures data and is found to outperform both the Cornell and French (CF, 1983a) and Yan (2002) models. The overall mean errors in terms of index points and percentages are 0.1918 and -0.002% for the FBR model, compared to -1.8806 and -0.2088% for the CF model, and 2.5072 and 0.0973% for the Yan model.

Levy subordinated hierarchical Archimedean copulas (LSHAC) are flexible models in high dimensional modeling. However, there is limited literature discussing their applications, largely due to the challenges in estimating their structures and their parameters. In this paper, we propose a three-stage estimation procedure to determine the hierarchical structure and the parameters of a LSHAC. This is the first paper to empirically examine the modeling performances of the LSHAC models using ex- change traded funds. Simulation study demonstrates the reliability and robustness of the proposed estimation method in determining the optimal structure. Empirical analysis further shows that, compared to elliptical copulas, LSHACs have better fitting abilities as well as more accurate out-of-sample Value-at-Risk estimates with less parameters. In addition, from a financial risk management point of view, the LSHACs have the advantage of being very flexible in modeling the asymmetric tail dependence, providing more conservative estimations of the probabilities of extreme downward co-movements in the financial market.

This paper proposes a new copula model known as the Levy subordinated hierarchical Archimedean copulas (LSHAC) for multi-country mortality dependence modeling. To the best of our knowledge, this is the first paper to apply the LSHAC model to mortality studies. Through an extensive empirical analysis on modelling mortality experiences of 13 countries, we demonstrate that the LSHAC model, which has the advantage of capturing the geographical structure of mortality data, yields better fit, more accurate and robust out-of-sample forecasting, when compared to other benchmark copula models. The LSHAC model also confirms that there is an association between geographical locations and dependence of the overall mortality improvement. These results yield new insights into future longevity risk management. Finally, the model is used to price a hypothetical survival index swap written on a weighted mortality index. The results highlight the importance of dependence modeling in managing longevity risk and reducing population basis risk.

Stock markets around the world have fallen sharply in recent years, leaving many stock options that were issued in better times deep out of the money. Some firms with employee stock options outstanding have chosen simply to adjust the strikes downward, toward current market levels. Reset options offer this kind of protection automatically, by specifying one or more stock price levels at which the option9s strike price will be reset. Liao and Wang examine the problem of pricing reset options, taking into account some real-world features, including multiple reset levels and arithmetic Asian payoffs, that may be present but present difficulties for valuation. They show how a standard reset contract may be valued as a package of barrier options, and they offer a control variate technique for Asian contracts. One important feature of reset options is the fact that delta is discontinuous at the reset points.

This article makes two contributions to the literature. The first contribution is to provide the closed-form pricing formulas of reset options with strike resets and predecided reset dates. The exact closed-form pricing formulas of reset options with strike resets and continuous reset period are also derived. The second contribution is the finding that the reset options not only have the phenomena of Delta jump and Gamma jump across reset dates, but also have the properties of Delta waviness and Gamma waviness, especially near the time before reset dates. Furthermore, Delta and Gamma can be negative when the stock price is near the strike resets at times close to the reset dates. © 2003 Wiley Periodicals, Inc. Jrl Fut Mark 23:87–107,2003

Motivated by the empirical findings that asset returns are autocorrelated, this paper provides the pricing algorithm for American options on the stocks, the returns of which depend on an autoregressive moving average (ARMA) process, by incorporating with the least squares Monte Carlo approach of Longstaff and Schwartz (2001) and the local risk-neutralization principle of Duan (1995). Based on the results of numerical analyses, the ARMA effect has significant impacts on values of American options. Specifically, the AR effect is more significant than the MA effect.

We develop an efficient distribution-based tree method to value a broad range of contingent claims under Gaussian HJM framework of stochastic interest rates. Instead of using random numbers from the standard normal at each time interval of Monte Carlo simulation, we use a zero-mean and unit-variance bell-shaped multinomial distribution to approximate the standard normal distribution. Based on these multinomial distributions, we create a multinomial distribution-based tree to implement for at least ten-years maturity American-style contingent claims with arbitrary deterministic volatilities of interest rates under multi-factor Gaussian HJM framework. From the numerical results, the distribution-based tree method can be used to compute options prices fast with accuracy.