Pricing Of Insurance Policies Research Articles

COPULA-BASED STATISTICAL MODELLING OF SYNOPTIC-SCALE CLIMATE INDICES FOR QUANTIFYING AND MANAGING AGRICULTURAL RISKS IN AUSTRALIA

Australia is an agricultural nation characterised by one of the most naturally diverse climates in the world, which translates into significant sources of risk for agricultural production and subsequent farm revenues. Extreme climatic events have been significantly affecting large parts of Australia in recent decades, contributing to an increase in the vulnerability of crops, and leading to subsequent higher risk to a large number of agricultural producers. However, attempts at better managing climate related risks in the agricultural sector have confronted many challenges. First, crop insurance products, including classical claim-based and index-based insurance, are among the financial implements that allow exposed individuals to pool resources to spread their risk. The classical claim-based insurance indemnifies according to a claim of crop loss from the insured customer, and so can easily manage idiosyncratic risk, which is the case where the loss occurs independently.Nevertheless, the existence of systemic weather risk (covariate risk), which is the spread of extreme events over locations and times (e.g., droughts and floods), has been identified as the main reason for the failure of private insurance markets, such as the classical multi-peril crop insurance, for agricultural crops. The index-based insurance is appropriate to handle systemic but not idiosyncratic risk. The indemnity payments of the index-based insurance are triggered by a predefined threshold of an index (e.g., rainfall), which is related to such losses. Since the covariate nature of a climatic event, it sanctions the insurers to predict losses and ascertain indemnifications for a huge number of insured customers across a wide geographical area. However, basis risk, which is related to the strength of the relationship between the predefined indices used to estimate the average loss by the insured community and the actual loss of insured assets by an individual, is a major barrier that hinders uptake of the index-based insurance. Clearly, the high basis risk, which is a weak relationship between the index and loss, destroys the willingness of potential customers to purchase this insurance product. Second, the impact of multiple synoptic-scale climate mode indices (e.g., Southern Oscillation Index (SOI) and Indian Ocean Index (IOD)) on precipitation and crop yield is not identical in different spatial locations and at different times or seasons across the Australian continent since the influence of large-scale climate heterogeneous over the different regions. The occurrence, role, and amplitude of synoptic-scale climate modes contributing to the variability of seasonal crop production have shifted in recent decades. These variables generally complicate the climate and crop yield relationship that cannot be captured by traditional modelling and analysis approaches commonly found in published agronomic literature such as linear regression. In addition, the traditional linear analysis is not able to model the nonlinear and asymmetric interdependence between extreme insurance losses, which may occur in the case of systemic risk. Relying on the linear method may lead to the problem that different behaviour may be observed from joint distributions, particularly in the upper and lower regions, with the same correlation coefficient. As a result, the likelihood of extreme insurance losses can be underestimated or overestimated that lead to inaccuracies in the pricing of insurance policies. Another alternative is the use of the multivariate normal distribution, where the joint distribution is uniquely defined using the marginal distributions of variables and their correlation matrix. However, phenomena are not always normally distributed in practice. It is therefore important to develop new, scientifically verified, strategic measures to solve the challenges as mentioned above in order to support mitigating the influences of the climate-related risk in the agricultural sector. Copulas provide an advanced statistical approach to model the joint distribution of multivariate random variables. This technique allows estimating the marginal distributions of individual variables independently with their dependence structures. It is clear that the copula method is superior to the conventional linear regression since it does not require variables have to be normally distributed and their correlation can be either linear or non-linear. This doctoral thesis therefore adopts the advanced copula technique within a statistical modelling framework that aims to model: (1) The compound influence of synoptic-scale climate indices (i.e., SOI and IOD) and climate variables (i.e., precipitation) to develop a probabilistic precipitation forecasting system where the integrated role of different factors that govern precipitation dynamics are considered; (2) The compound influence of synoptic-scale climate indices on wheat yield; (3) The scholastic interdependencies of systemic weather risks where potential adaptation strategies are evaluated accordingly; and (4) The risk-reduction efficiencies of geographical diversifications in wheat farming portfolio optimisation. The study areas are Australia’s agro-ecological (i.e., wheat belt) zones where major seasonal wheat and other cereal crops are grown. The results from the first and second objectives can be used for not only forecasting purposes but also understanding the basis risk in the case of pricing climate index-based insurance products. The third and fourth objectives assess the interactions of drought events across different locations and in different seasons and feasible adaptation tools. The findings of these studies can provide useful information for decision-makers in the agricultural sector. The first study found the significant relationship between SOI, IOD, and precipitation. The results suggest that spring precipitation in Australia, except for the western part, can be probabilistically forecasted three months ahead. It is more interesting that the combination of SOI and IOD as the predictors will improve the performance of the forecast model. Similarly, the second study indicated that the largescale climate indices could provide knowledge of wheat crops up to six months in advance. However, it is noted that the influence of different climate indices varies over locations and times. Furthermore, the findings derived from the third study demonstrated the spatio-temporally stochastic dependence of the drought events. The results also prove that time diversification is potentially more effective in reducing the systemic weather risk compared to spatially diversifying strategy. Finally, the fourth objective revealed that wheat-farming portfolio could be effectively optimised through the geographical diversification. The outcomes of this study will lead to the new application of advanced statistical tools that provide a better understanding of the compound influence of synoptic-scale climatic conditions on seasonal precipitation, and therefore on wheat crops in key regions over the Australian continent. Furthermore, a comprehensive analysis of systemic weather risks performed through advanced copula-statistical models can help improve and develop novel agricultural adaptation strategies in not only the selected study region but also globally, where climate extreme events pose a serious threat to the sustainability and survival of the agricultural industry. Finally, the evaluation of the effectiveness of diversification strategies implemented in this study reveals new evidence on whether the risk pooling methods could potentially mitigate climate risks for the agricultural sector and subsequently, help farmers in prior preparation for uncertain climatic events.

Pricing of insurance policies against cloud storage price rises

When a company migrates to cloud storage, the way back is neither fast nor cheap. The company is then locked up in the storage contract and exposed to upward market prices, which reduce the company's profit and may even bring it below zero. We propose a protection means based on an insurance contract, by which the cloud purchaser is indemnified when the current storage price exceeds a pre-defined threshold. By applying the financial options theory, we provide a formula for the insurance price (the premium). By using historical data on market prices for disks, we apply the formula in realistic scenarios. We show that the premium grows nearly quadratically with the duration of the coverage period as long as this is below one year, but grows more slowly, though faster than linearly, over longer coverage periods.

Capital Allocation for Insurance Companies: Issues and Methods

We address some key issues related to risk and capital allocation in insurance companies. We argue that the Froot-Stein approach to risk is relevant to a number of important problems in the daily management of an insurance portfolio and that - taken to its consequence - this approach will lead to a close co-operation between actuarial and financial departments with a particular view to the actuaries ability to separate financial risk from insurance risk and the ability of the finance department to hedge the right amount of their complicated financial risk at a good price. Further, we introduce a new capital allocation principle based on the solvency of the entire company and we claim that this principle is more robust than traditional methods. We also introduce a new way of combining capital allocation and pricing of insurance policies. Through a performance measure of return on capital, we suggest a way of evaluating the price of capital for a single policy, that this money is held as a reserve and that this reserve should run off in such a way that old underwriting does not harm the performance of any given business line.

Insurance Premium Pricing and Ratemaking in Competitive Insurance and Capital Asset Markets

This paper develops an equilibrium model of insurance pricing integrating both the insurance and capital asset markets from the insurers' viewpoint. In contrast to the capital assets based models, it emphasizes the importance of the insurance market, i.e., the claim payments by all insurers as a whole, in pricing insurance premiums. The premium for insurance is found to be a function of both the systematic insurance market risk and the systematic capital market risk. An important practical implication of this model is that the fair profit rates for most lines of insurance should be higher than those recommended by current models based on the CAPM. The purpose of this paper is to develop a general equilibrium model of insurance premium pricing under both competitive insurance and capital markets. Largely motivated by the need to find alternative solutions to the fair-rate-of-return problem, several researchers have applied the asset pricing models to insurance premium pricing. In particular, Cooper [4] develops and tests a model based on the portfolio theory. Biger and Kahane [2], Hill [8], and Fairley [6], Urrutia [15] applies the Capital Asset Pricing Model [CAPM] approach, while Kraus and Ross [10] adapts the Arbitrage Pricing Theory [APT] to the insurance case. Because these models are borrowed from the finance literature where the market of interest is the asset market, they share a common shortcoming: it is concerned mainly with the systematic risks associated with the asset market. The insurance market, ironically, is ignored. From the balance sheet relationship that equity is the residual claim in which the asset return is netted out by the insurance loss, the expected return on the insurance company equity is expressed as a function of both the systematic risk of the insurance portfolio with the asset market portfolio and the James S. Ang is the William 0. Cullom Professor of Finance at the Florida State University. He received his Ph.D. from Purdue University. Dr. Ang has published estensively in Finance and Economics Journals. Tsong-Yue Lai is an Assistant Professor of Finance at the Florida State University. He received his Ph.D. from Yale University. This content downloaded from 207.46.13.120 on Thu, 15 Sep 2016 05:41:45 UTC All use subject to http://about.jstor.org/terms 768 The Journal of Risk and Insurance systematic risk of the investment portfolio with the asset market portfolio, e.g., [2], [6], [8]. However, it is important to note that in these models, the fair-rate-of-return for ratemaking purposes or the premium for pricing an insurance policy is a function of only the systematic risk of that insurance policy and the asset market [see equation (9) of Biger and Kahane [2], equation (8) of Hill [8], and equation (11) of Fairley [6]). From the insurance industry viewpoint, there are not one but two important markets. The first is the familiar asset market which encompasses all assets, traded or nontraded, that are held. The second, equally important but often neglected market, is the insurance market. The difference between these two markets is not trivial. The asset market has a positive net supply, while the insurance market has a zero net supply. In other words, if all the asset portfolios are aggregated, the resulting figure is the wealth of the economy. An increase (decrease) in the aggregate wealth (or shares of IBM) leads to a corresponding increase (decrease) of those who hold a diversified portfolio (or shares of IBM). On the other hand, an insurance policy is a contract between the insurer and the insured. When a loss occurs, money is transferred from the insurer to the insured. Wealth is being redistributed but the aggregate does not increase. Although it is tempting to include all insurance contracts in the definition of the asset market portfolio, it will not work. Because a zero net supply exists for each insurance policy, and for the insurance market as a whole, the distribution of wealth between the suppliers (insurer) and the demanders (the insured) has absolutely no effect on the asset market portfolio, i.e., the asset market portfolio will behave as if no insurance contracts existed. Here, a troubling question arises: if the insurance market does not affect the asset market portfolio, can it be ignored in the pricing of insurance policies? The answer is no. If needs for insurance exist in the society, individuals and insurers must either be suppliers or demanders of a particular type of insurance policy. Thus, insurance contracts, which are netted out in the aggregate, are in positive net supply or demand for individuals and insurers. Specifically, the insurers, being net suppliers of insurance, cannot ignore the aggregate insurance loss (payments on all insurance claims in a given period) in the pricing of insurance policies. For insurers with a diversified insurance portfolio, e.g., multi-line insurers and their competitors, i.e., all single line insurers, it is reasonable to expect that the price or premium on a policy, whose claim arises in a period when the aggregate insurance claim is high, i.e., a positive correlation with the aggregate insurance market, should also be high. In this case a higher premium is charged because the insurer is less able to shoulder the payment of many claims at the same time. The risk includes financial insolvency as well as possible ruin. This intuition is formally developed in an integrated model of insurance and capital markets. The model gives a pricing equation for an insurance premium which may be used for the calculation of the fair-rate-of-return. It is shown that this model generates all other models of insurance premium pricing in competitive markets as special cases. Conclusions are presented in the last section. This content downloaded from 207.46.13.120 on Thu, 15 Sep 2016 05:41:45 UTC All use subject to http://about.jstor.org/terms Insurance Premium Pricing and Ratemaking 769