Transparency in the Mortgage Market

This paper studies the impact of transparency in the mortgage market on the underlying real estate market. We show that geographic transparency in the secondary mortgage market, which implies geographic risk based pricing in the primary market, can limit risk-sharing and make house prices more volatile. Ex ante, regions prefer opaque markets to enable insurance opportunities. We discuss the implications for risk based pricing and house price volatility more generally. In addition, we investigate the specific conditions under which competitive lenders would optimally choose to provide opaque lending, thus reducing volatility in the real estate market. We show that in general the opaque competitive equilibrium is not stable, and lenders have incentive to switch to transparent lending if one of the geographic regions has experienced a negative income shock. We propose market and regulatory mechanisms that make the opaque competitive equilibrium stable and insurance opportunities possible.     

Catastrophe Risk Bonds

Abstract

This article examines the pricing of catastrophe risk bonds. Catastrophe risk cannot be hedged by traditional securities. Therefore, the pricing of catastrophe risk bonds requires an incomplete markets setting, and this creates special difficulties in the pricing methodology. The authors briefly discuss the theory of equilibrium pricing and its relationship to the standard arbitrage-free valuation framework. Equilibrium pricing theory is used to develop a pricing method based on a model of the term structure of interest rates and a probability structure for the catastrophe risk. This pricing methodology can be used to assess the default spread on catastrophe risk bonds relative to traditional defaultable securities.     

Equilibrium Pricing of General Insurance Policies

Abstract

A model is developed for determining the price of general insurance policies in a competitive, noncooperative market. This model extends previous single-optimizer pricing models by supposing that each participant chooses an optimal pricing strategy. Specifically, prices are determined by finding a Nash equilibrium of an N-player differential game. In the game, a demand law describes the relationship between policy sales and premium, and each insurer aims to maximize its (expected) utility of wealth at the end of the planning horizon. Two features of the model are investigated in detail: the effect of limited total demand for policies, and the uncertainty in the calculation of the breakeven (or cost price) of an insurance policy.

It is found that if the demand for policies is unlimited, then the equilibrium pricing strategy is identical for all insurers, and it can be found analytically for particular model parameterizations. However, if the demand for policies is limited, then, for entrants to a new line of business, there are additional asymmetric Nash equilibria with insurers alternating between maximal and minimal selling. Consequently it is proposed that the actuarial cycle is a result of price competition, limited demand, and entry of new insurers into the market. If the breakeven premium is highly volatile, then the symmetric equilibrium premium loading tends to a constant, and it is suggested that this will dampen the oscillatory pricing of new entrants.     

Equilibrium in a reinsurance market: Introducing taxes

We introduce profit taxation in Borch's [1962] model of a competitive insurance market. We analyze the impact of taxation on equilibrium prices and characterize the cases where optimal risk sharing is preserved. In the case of Constant Relative Risk Aversion (CRRA) utility functions, this abstract characterization is translated into simple conditions involving the solvency ratios of the companies. The case of Constant Absolute Risk Aversion (CARA) utility functions is also studied.     

Pricing and managing risks of European-style options in a Markovian regime-switching binomial model

We discuss the pricing and risk management problems of standard European-style options in a Markovian regime-switching binomial model. Due to the presence of an additional source of uncertainty described by a Markov chain, the market is incomplete, so the no-arbitrage condition is not sufficient to fix a unique pricing kernel, hence, a unique option price. Using the minimal entropy martingale measure, we determine a pricing kernel. We examine numerically the performance of a simple hedging strategy by investigating the terminal distribution of hedging errors and the associated risk measures such as Value at Risk and Expected Shortfall. The impacts of the frequency of re-balancing the hedging portfolio and the transition probabilities of the modulating Markov chain on the quality of hedging are also discussed.     

Income Insurance and the Equilibrium Term Structure of Equity

Output, wages, and dividends feature term structures of variance ratios that are respectively flat, increasing, and decreasing. Income insurance from shareholders to workers explains these term structures. Risk‐sharing smooths wages but only concerns transitory risk and hence enhances short‐run dividend risk. As a result, actual labor‐share variation largely forecasts the risk, premium, and slope of dividend strips. A simple general equilibrium model in which labor rigidity affects dividend dynamics and the price of short‐run risk reconciles standard asset pricing facts with the term structures of the equity premium, volatility, and macroeconomic variables, which are at odds in leading models.     

Pricing financial services innovations

The number of innovative financial solutions introduced to markets has grown considerably in the past decade owing to emerging digital technologies, deregulation and market fragmentation. Examples are abundant in the worldwide markets for insurance, credit products and transaction processing services. A question of growing interest is how firms should price these innovations. The optimal introductory pricing of financial innovations may vary as a function of factors such as price sensitivity of the market and competitors’ ability to introduce competing financial solutions. In this article, we examine the role of these factors in the optimal pricing of a financial innovation. Using an agent-based simulation framework, introductory pricing strategies that maximize profitability under various market conditions are identified. Results indicate that lower levels of market price sensitivity and longer time horizons for competitive entry create pricing opportunities for financial innovators. However, the relationship becomes more complex as market price sensitivity increases or competitive market entry becomes more immediate. Detailed recommendations for optimal pricing of financial innovations under various market conditions are provided, and the article concludes with strategic recommendations for pricing innovative financial services.     

Hidden insurance in a moral‐hazard economy

We analyze the general equilibrium of an economy in which a competitive industry produces nonexclusive insurance services. The equilibrium is inefficient because insurance contracts cannot control moral hazard, and welfare can be improved by policies that reduce insurance by increasing its price above marginal cost. We discuss how insurance production costs that exceed expected claim payments interact with moral hazard in determining the equilibrium's inefficiency, and show that these costs can make insurance premia so actuarially unfair as to validate the standard first‐order conditions we exploit in our analysis.     

The Capital Structure of Firms Subject to Price Regulation: Evidence from the Insurance Industry

Automobile and workers' compensation insurance are relatively homogeneous products sold under varying regulatory systems among the states. This paper investigates how price regulation affects the capital structure decisions of profit-maximizing insurers who sell insurance in both competitive and/or regulated markets. Specifically, we test the hypothesis that insurers subject to price regulation will choose to hold less capital. In addition, we hypothesize insurers subject to more stringent regulatory pricing constraints will choose even higher degrees of leverage because the benefits of holding additional amounts of capital are suppressed. We conduct empirical tests using cross-sectional data on insurers and find evidence consistent with both hypotheses. These findings have important implications for insurance price and solvency regulation. Stricter price regulation increases the default risk (i.e., reduces the financial quality) of insurance contracts purchased by individuals and firms.     

Designing feasible and effective health plan payments in countries with data availability constraints

Risk equalization schemes, which transfer money to/from insurers that have above/below average risks, are a fundamental tool in regulated health insurance markets in many countries. Risk sharing (the transfer of some responsibility for costs from a plan to the regulator or the overall insurance market), are an additional method of insulating insurers who attract higher-than-average risks. This paper proposes, implements and quantifies incorporating risk sharing within a risk equalization scheme that can be applied in a data-poor context. Using Chile's private health insurance market as case study, we show that modest amount of risk sharing greatly improves fit even in simple demographic-based risk equalization. Expanding the model's formula to include morbidity-based adjustors and risk sharing redirects compensations at insurer level and reduces opportunity to engage in profitable risk selection at the group level. Our emphasis on feasibility may make alternatives proposed attractive to countries facing data-availability constraints.     

Analytical Approach to Value Options with State Variables of a Levy System

In this paper we present an analytical method in pricing Europeancontingent assets, whose state variables follow a multi-dimensionalLévy process. We give an explicit formula for the hypotheticalEuropean "two-price" call option price by means of the conditionacharacteristic transform. The work not only unifies and extendsthe option pricing literature, which focuses on the use of thecharacteristic function, but also provides the way to formalizeandunify the valuation of the option price, the valuation of thediscount bond price, the valuation of the scaled-forward price,and the valuation of the pricing measure in incomplete markets.JEL Classification codes: G13     

An Actuarial Premium Pricing Model for Nonnormal Insurance and Financial Risks in Incomplete Markets

Abstract

A model for pricing insurance and financial risks, based on recent developments in actuarial premium principles with elliptical distributions, is developed for application to incomplete markets and heavy-tailed distributions. The pricing model involves an application of a generalized variance premium principle from insurance pricing to the pricing of a portfolio of nontraded risks relative to a portfolio of traded risks. This pricing model for a portfolio of insurance or financial risks reflects preferences for features of the distributions other than mean and variance, including kurtosis. The model reduces to the Capital Asset Pricing Model for multinormal portfolios and to a form of the CAPM in the case where the traded and nontraded risks have the same elliptical distribution.     

Time-consistent reinsurance and investment strategies for an AAI under smooth ambiguity utility

This paper investigates time-consistent reinsurance(excess-of-loss, proportional) and investment strategies for an ambiguity averse insurer(abbr. AAI). The AAI is ambiguous towards the insurance and financial markets. In the AAI's attitude, the intensity of the insurance claims' number and the market price of risk of a stock can not be estimated accurately. This formulation of ambiguity is similar to the uncertainty of different equivalent probability measures. The AAI can purchase excess-of-loss or proportional reinsurance to hedge the insurance risk and invest in a financial market with cash and an ambiguous stock. We investigate the optimization goal under smooth ambiguity given in Klibanoff, P., Marinacci, M., & Mukerji, S. [(2005). A smooth model of decision making under ambiguity. Econometrica 73, 1849–1892], which aims to search the optimal strategies under average case. The utility function does not satisfy the Bellman's principle and we employ the extended HJB equation proposed in Björk, T. & Murgoci, A. [(2014). A theory of Markovian time-inconsistent stochastic control in discrete time. Finance and Stochastics 18(3), 545–592] to solve this problem. In the end of this paper, we derive the equilibrium reinsurance and investment strategies under smooth ambiguity and present the sensitivity analysis to show the AAI's economic behaviors.     

“Analysis of Incremental Returns of Canadian Mutual Funds”, J. F. Carrière; C. F. Hill,April 2001

Abstract

The determination and allocation of economic capital is important for pricing, risk management, and related insurer financial decision making. This paper considers the allocation of economic capital to lines of business in insurance. We show how to derive closed-form results for the complete markets, arbitrage-free allocation of the insurer default option value, or insolvency exchange option, to lines of business for an insurer balance sheet. We assume that individual lines of business and the surplus ratio are joint log-normal although the method we adopt allows other assumptions. The allocation of the default option value is required for fair pricing in the multiline insurer. We discuss and illustrate other methods of capital allocation, including Myers-Read, and give numerical examples for the capital allocation of the default option value based on explicit payoffs by line.     

Pricing currency risk in the stock market: Evidence from Finland and Sweden 1970-2009

We investigate the role of currency risk on stock markets in two interlinked Nordic countries exhibiting a gradual move from fixed to floating exchange rates. We apply the Ding and Engle (2001) covariance stationary specification in a multivariate GARCH-M setup to test a conditional international asset pricing model. Using a sample period from 1970 to 2009, we find that the currency risk is priced in both stock markets, and that the price and the risk premium are lower after the floatation of the currencies, especially for Finland. We also find the cross-country exchange rate shock from Finland to affect the price of currency risk in Sweden, but not vice versa. Finally, we discuss some of the potential issues in applying multivariate GARCH-M specifications in tests of asset pricing models.     

The Dynamics of Insurance Prices

We develop a continuous-time general-equilibrium model to rationalise the dynamics of insurance prices in a competitive insurance market with financial frictions. Insurance companies choose underwriting and financing policies to maximise shareholder value. The equilibrium price dynamics are explicit, which allows simple numerical simulations and generates testable implications. In particular, we find that the equilibrium price of insurance is (weakly) predictable and the insurance sector always realises positive expected profits. Moreover, rather than true cycles, insurance prices exhibit asymmetric reversals caused by the reflection of the aggregate capacity process at the dividend and recapitalisation boundaries.     

Nonlinear Cointegration Relationships Between Non-Life Insurance Premiums and Financial Markets

The aim of this article is to study the adjustment dynamics of the non-life insurance premium (NLIP) and test its dependence to the financial markets in five countries (Canada, France, Japan, the United Kingdom, and the United States). First, we justify the linkage between the insurance and the financial markets by the underwriting cycle theory and financial models of insurance pricing. Second, we examine the relationship between the NLIP, the interest rate, and the stock price using the recent developments of nonlinear econometrics. We use threshold cointegration models: the switching transition error correction models (STECM). We show that STECM perform better than a linear error correction model (LECM) to reproduce the NLIP dynamics. Our empirical results show that the adjustment of the NLIP in France, Japan, and the United States is rather discontinuous, asymmetrical, and nonlinear. Moreover, we suggest a strong evidence of significant linkages between insurance and financial markets, show two regimes for the NLIP, and find that the NLIP adjustment toward equilibrium is time varying with a convergence speed that varies according to the insurance disequilibrium size.     

Complete Versus Incomplete Insurance Contracts under Adverse Selection with Multiple Risks

This article extends the standard adverse-selection model for competitive insurance markets, which assumes a single source of risk, to the case where individuals are subject to multiple risks. We compare the following market situations—the case where insurers can offer comprehensive policies against all sources or risks (complete contracts) and the case where different risks are covered by separate policies (incomplete contracts). In the latter case, we consider whether the insurer of a particular risk has perfect information regarding an individual's coverage against other sources of risks. The analysis emphasizes the informational role of bundling in multidimensional screening. When the market situation allows bundling, it is shown that in equilibrium the low-risk type with respect to a particular source of risk does not necessarily obtain partial coverage against that particular risk.     

Pricing Dynamic Insurance Risks Using the Principle of Equivalent Utility

We introduce an expected utility approach to price insurance risks in a dynamic financial market setting. The valuation method is based on comparing the maximal expected utility functions with and without incorporating the insurance product, as in the classical principle of equivalent utility. The pricing mechanism relies heavily on risk preferences and yields two reservation prices - one each for the underwriter and buyer of the contract. The framework is rather general and applies to a number of applications that we extensively analyze.     

Asset market equilibrium with liquidity risk

This paper derives an equilibrium asset pricing model with endogenous liquidity risk. Liquidity risk is modeled as a stochastic quantity impact on the price from trading, where the size of the impact depends on trade size. Under a strong set of assumptions, we prove that a unique equilibrium liquidity cost process and a unique equilibrium price process exists for our economy. We characterize the market’s state price density, which enables the derivation of the risk-return relation for the stock’s expected return including liquidity risk. We derive a generalized intertemporal CAPM and consumption CAPM for these markets. In contrast to the traditional models without liquidity risk, there is an additional systematic liquidity risk factor which is related to the stock return’s covariation with the market’s stochastic liquidity cost. Traditional transaction costs are a special case of our formulation.