PUBLICATION

While the COVID-19 pandemic has shattered the world with severe human toll and catastrophic economic losses and sufferings, it has also heightened the need for more effective solutions for managing epidemic-related risks. In this paper, we pro- pose two capital market-based epidemic financing facilities to address two extremes of epidemic risks. The proposed pandemic bond is meant to hedge the severe pandemic outbreak while the proposed endemic swap can be used to hedge a recurrent endemic. Using coronavirus as an example of a pandemic and dengue fever as an example of an endemic, we discuss the modeling and pricing of the proposed epidemic securities. We price the proposed securities based on epidemiological models as well as actuarial models. We show that the proposed hedging securities can provide additional capital relief for pandemic recovery plans, effectively stablize hedgers’ cash flows, and create attractive returns to different investors.

Keywords: Securitization, Pandemic bond, Endemic swap, Coronavirus, Dengue 

Domestic tourism demand has dominated the global tourism market and has been more resilient during the COVID-19 pandemic; yet, it is under-studied compared to international tourism demand. Digital financial inclusion (DFI) enables the provision of formal financial products and services to small and medium-sized tourism enterprises and tourists through cost-effective digital means, potentially boosting domestic tourism demand. Integrating micro- and macro-level data from 335 prefecture-level regions in China, we investigate the impact of DFI on domestic tourism demand using spatial panel models. Our analysis reveals significant and positive effects, both direct and spillover, of DFI on domestic tourism demand within a region and across regions. Notably, among the three dimensions of DFI, the usage depth exhibits the most substantial spillover effects. Furthermore, our findings also highlight the crucial role of DFI in internalizing domestic tourism revenues. Our study provides practical implications for sustainable domestic tourism development in the digital era. 

Keywords: Digital financial inclusion; domestic tourism demand; spatial spillover; spatial economics; sustainable tourism development 

We propose a new machine learning-based framework for long-term mortality forecasting. Based on ideas of neighbouring prediction, model ensembling, and tree boosting, this framework can significantly improve the prediction accuracy of long-term mortality. In addition, the proposed framework addresses the challenge of a shrinking pattern in long-term forecasting with information from neighbouring ages and cohorts. An extensive empirical analysis is conducted using various countries and regions in the Human Mortality Database. Results show that this framework reduces the mean absolute percentage error (MAPE) of the 20-year forecasting by almost 50\% compared to classic stochastic mortality models, and it also outperforms deep learning-based benchmarks. Moreover, including mortality data from multiple populations can further enhance the long-term prediction performance of this framework.

Keywords: long-term mortality forecasting; neighbourhood effect; machine learning; ensemble models; tree boosting; longevity risk

In the past decade, cyber risk has raised much interest in the economy, and cyber risk has evolved from a type of pure operational risk to both operational and liability risk. However, the modeling of cyber risk is still in its infancy. Compared with other financial risks, cyber risk has some unique features. In particular, discrete variables regularly arise both in the frequency component (e.g. number of events per unit time), and the severity component (e.g. the number of data breaches for each cyber event). In addition, the modeling of these count variables are further complicated by nonstandard properties such as zero inflation, serial and cross-sectional correlations, as well as heavy tails. Previous cyber risk models have largely focused on continuous models that are incompatible with many of these characteristics. This paper introduces a new count-based frequency-severity framework to model cyber risk, with a dynamic multivariate negative binomial autoregressive process for the frequency component, and the generalized Poisson inverse-Gaussian distribution for the severity component. We unify these new modeling tools by proposing a tractable Generalized Method of Moments for their estimation and apply them to the Privacy Rights Clearinghouse (PRC) dataset. 

Keywords: Operational risk, Cyber risk, Systemic and pairwise contagion, Self-excitation, Negative binomial autoregressive process, Generalized Poisson inverse-Gaussian distribution, Discrete stable distribution 

Both the frequency and intensity of weather-related catastrophes, such as storms and floods, have been increasing due to climate change such as global warming. This leads to rising storm catastrophe risks faced by the property & casualty insurance and reinsurance sector. This research proposes an index-based storm catastrophe (CAT) bond for reinsurers to hedge catastrophe risks related to storm losses. Storm losses data have a large portion of zero values and a continuous positive right-skewed distri- bution, together with high-dimensional spatial dependence. We address these unique properties by proposing a Gamma-two-part-autoregressive (Gamma-2PAR) distribution as the marginal model, and the spatio-temporal vine copula as the dependence model. We investigate the CAT bond market equilibrium and endogenously solve for the optimal market price of risk and coupon rates. Our empirical results using historical losses data at the county-level in Florida show the proposed CAT bond can stabilize the reinsurer’s cash flows and create attractive returns to investors by offering high coupon rates. Our framework can be generalized to design and price other catastrophe financing facilities.

Keywords: climate change; catastrophe risk; CAT bond; spatio-temporal copula; storm losses 

Effective agricultural insurance and risk management program rely on accurate crop yield forecasting. In this paper, we propose a novel deep factor model for crop yield forecasting and crop insurance ratemaking. This framework first utilizes a deep autoencoder to extract a latent factor, called production index, which integrates salient spatial temporal patterns in the original yield data. Then, a concatenated deep learning model is constructed to enhance the modeling of the production index and the reconstruction of crop yields. Convolutional neural networks are employed to capture the high-dimensional and highly nonlinear structure within the crop yield data, as well as its interactions with weather and economic variables. The proposed deep factor framework is applied to the county-level data in the state of Iowa, U.S. Empirical results show that the newly proposed deep factor model significantly improves the prediction accuracy, especially in the test set. Based on a retain-cede crop insurance rating game between a private insurer and the government, we show that the proposed deep factor model provides economically and statistically significant improvement over the current RMA ratemaking methodology.

Keywords: agricultural insurance; autoendocer; convolutional neural network; deep learning; ratemaking

This paper provides a flexible multi-factor framework to address some ongoing challenges in mortality modeling, with a special focus on the mortality curvature and possible mortality plateau for extremely old ages. We extend the Gompertz law Gompertz (1825) by proposing a multi-factor exponential model. The proposed framework is based on the Laguerre approximating functions, and is able to capture flexible mortality patterns, and allows for a convenient estimation and prediction algorithm. An extensive empirical analysis is conducted using the proposed framework with a merged mortality database containing a large number of countries and regions with credible old-age mortality data. We find that the proposed exponential model leads to superior goodness-of-fit to historical data, and better out-of-sample forecast performance. Moreover, the exponential model predicts more balanced mortality improvements across ages, and thus leads to higher projected remaining life expectancy for the old ages than existing Gompertz-based mortality models. Finally, the modeling capacity of the proposed exponential model is further demonstrated by a multi-population extension, and an illustrative example of estimation and forecast is provided.

Keywords: Old Age Mortality Forecasting, Gompertz Law, Factor Model

Accurate crop yield forecasting is central to effective risk management for many stakeholders, including farmers, insurers, and governments, in various practices, such as crop management, sales and marketing, insurance policy design, premium rate setting, and reserving. This paper rst investigates an innovative approach of yield forecasting using a dynamic factor model. Based on the proposed approach, we then design an enhanced weather index-based insurance (IBI) policy. The dynamic factor approach is motivated by its ability to effectively summarize the information in a large set of explanatory variables with common factors of a much lower dimension. This makes it possible to use an extensive set of variables in crop yield prediction without worrying about identication issues. Using both county-level and state-level crop production data from the state of Illinois, U.S., the empirical results show that the dynamic factor approach produces more accurate in- and out-of-sample forecasting results compared to the classical statistical models. The empirical results also support that the proposed IBI policy based on the dynamic forecasting model has small basis risk. This, in turn, greatly improves the IBI's hedge effectiveness against agricultural production as well as increases its practicality as an insurance policy for agriculture.

Keywords: Crop Yield Forecasting; Factor Model; Index-based Insurance

We contribute to the non-life experience ratemaking literature by introducing a computationally efficient approximation algorithm for the Bayesian premium in models with dynamic random effect, where the risk of a policyholder is governed by an individual process of unobserved heterogeneity. We propose to approximate the dynamics of the random effect process by a discrete (hidden) Markov chain, and replace the intractable Bayesian premium of the original model by that of the approximate Markov chain model, for which concise, closed form formula are derived. The methodology is general as it does not rely on any parametric distributional assumptions, and in particular allows for the inclusion of both the cost and the frequency components in pricing. Numerical examples show that the proposed approximation method is highly accurate. Finally, a real-data pricing example is used to illustrate the versatility of the approach.

Keywords: Markov Chain Discretization; Bayesian Premium; Dynamic Random Effect; Risk Heterogeneity

Weather index insurance is a relatively new alternative to traditional agricultural insurance. It is still mostly at the experimental stage, rather than widespread in use like traditional crop insurance. A major challenge for weather insurance is basis risk, where the loss estimated by the index differs from the actual loss, and this is generally believed to be the main limitation in the use of weather index insurance for crops. Variable basis risk is an important type of basis risk that occurs when there are incorrect variables or missing variables for the design of the weather index. In agriculture, there is a relatively small sample size of yields, therefore, as the number of considered weather variables increases, the problems of limited degrees of freedom for predictive models must be overcome. The objective of this paper is to demonstrate two possible approaches that could be used to construct a multivariable weather index to reduce variable basis risk. Forage insurance is used as an example, and a main focus of the research is on reducing the dimensionality of the predictive model and resolving the problem of multicollinearity among weather variables. The research uses daily weather information and county-level forage yield data from Ontario, Canada. Two multivariable indices are developed based on principal component regression (PCR) and partial least squares regression (PLSR) methods, and they are evaluated against a single variable benchmark index based on cumulative precipitation (SVCP) using several basis risk metrics. The results show that both the PCR and PLSR models are superior compared to the SVCR index, and can be used to achieve the objective of reducing the dimensionality of the weather variable matrix and addressing the issue of multicollinearity. While the PLSR indices perform better than the PCR and SVCR indices in terms of average value of basis risk (E(BRLoss)), the PCR method produces a smaller percentage of mismatch, suggesting that the PCR method may be superior in correctly detecting when the insurance payment should be triggered. The methods demonstrated in this paper will assist in the development of weather index-based crop insurance.

Index insurance for crops is still at a relatively infant stage, and more research and development is needed in order to address a main limitation, which is referred to as basis risk (the mismatch between the loss indicated by the index and the actual loss suffered by the insured). Traditionally ground weather station measurements have been the most common approach used in weather indices, and this approach has often led to high levels of basis risk. Recent advances in satellite-based remote sensing provides new opportunities to use publicly available and transparent “big data”, to potentially make index-based insurance policies more relevant by reducing basis risk. This is the first paper to provide a comprehensive comparison of thirteen Pasture Production Indices (PPI's), including those developed based on satellite-derived vegetation and biophysical parameter indices using data products from the Moderate Resolution Imaging Spectroradiometer - MODIS. A validation protocol is established, and a unique dataset covering the period from 2002 to 2016 from a network of pasture clip sites in the province of Alberta, Canada is used to demonstrate new applications for insurance based on remote sensing derived data.

Keywords: Crop Yield Prediction; Forage Insurance; Remote Sensing; Index-Based Insurance; Principal Component Analysis; Predictive Analytics

A new relational data-matching model is presented to predict individual farmer yields in the absence of farm-level data. The relational model defines a similarity measure based on an Euclidean distance metric that considers weather information, farm size, county size and the coefficient of variation of yield, to search for the most "similar" region in a different country to borrow individual loss experience data that is otherwise not available. Detailed farm-level and county-level corn yield data in Canada and the U.S. are used to empirically evaluate the proposed relational model. The results show that the model achieves lower mean and standard deviation prediction errors and recovers the actual premium rate more accurately compared to the benchmark model. This research provides a new approach for insurers, reinsurers and governments to enhance individual loss experience, helping to overcome issues such as data scarcity and credibility, as well as aggregation bias, that present substantial challenges in risk modelling, pricing and developing new insurance programs, particularly in developing countries.

Keywords: Relational Model, Aggregation Bias, Shortness of Data, Euclidean Distance, Crop Insurance, Yield Forecasting, Ratemaking

The objective of this paper is to formally introduce premium principles to the agricultural insurance literature, with a focus on a new premium principle approach based on the multivariate weighted distribution. The multivariate weighted premium principle (MWPP) formalizes the reweighting of historical loss experience using external factors in order to refine the agricultural insurance pricing. These external factors may reflect systemic risk and include material information, such as economic and market conditions, weather, soil, etc. In the empirical study, a unique reinsurance data set from the province of Manitoba, Canada, is used to evaluate a number of potential premium principles. With the flexibility of the MWPP, the empirical results indicate that the MWPP approach can be a viable premium principle for pricing agricultural insurance. Furthermore, the MWPP redistributes premium rates and assigns increased loadings to higher risk layers, helping reinsurers manage their reserves and achieve improved sustainability in the long term. 

Keywords: Agricultural insurance; Loss reweighting; Ratemaking; Premium principles; Weighted distribution; Weighed premium

The agriculture sector relies on insurance and reinsurance as a mechanism to spread loss. Possible changes in climate, such as an increase in the frequency and severity of spatially correlated weather events, may lead to increased insurance costs. In some cases the structure of risk-sharing arrangements between governments and the private sector, which have historically proven important in the successful delivery of crop insurance programs in many countries, may also be impacted. This paper proposes a new reinsurance pricing framework, including a new crop yield forecasting model that integrates weather variables and crop production information from different geographically correlated regions using a new credibility estimator, and closed form reinsurance pricing formulas. The model is empirically analyzed, with an original comprehensive weather index system, and algorithms that combine screening regression (SR), cross validation (CV) and principal component analysis (PCA) to achieve efficient dimension reduction and model selection. The results show that the forecasting model has significantly improved the classical regression model, in term of both in-sample and out-of-sample forecasting abilities. Based on this framework, agricultural insurers and reinsurers may also develop improved weather risk management strategies to help manage adverse weather events. 

Keywords: Credibility; Reinsurance Pricing; Ratemaking; Model Selection

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 Levy subordinated hierarchical Archimedean copula (LSHAC) model in modelling the spatial dependence of weather risk to reduce basis risk. The analysis shows that the LSHAC model can improve the hedging performance through more accurate modelling of the dependence structure of weather risks and is more effcient 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. 

Keywords: Systemic weather risk; Hedging strategies; Hierarchical Archimedean copulas; Lévy subordinators

Lévy 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 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. 

Keywords: High dimensional modeling; Hierarchical Archimedean copulas; Lévy subordinators, Downside risk

This paper comprehensively examines the ratemaking process, including reviews of different detrending methods and the generating process of the historical loss cost ratio's (LCR's, which is defined as the ratio of indemnities to liabilities). A modified credibility approach is developed based on the Erlang mixture distribution and the liability weighted LCR. In the empirical analysis, a comprehensive data set representing the entire crop insurance sector in Canada is used to show that the Erlang mixture distribution captures the tails of the data more accurately compared to conventional distributions. Further, the heterogeneous credibility premium based on the liability weighted LCR’s is more conservative, and provides a more scientific approach to enhance the reinsurance pricing. 

Keywords: Erlang mixture; Credibiilty; EM Algorithm; Reinsurance Ratemaking