Portfolio Insurance Strategies when Hedging Affects Share Prices

Option-based portfolio insurance can result in coordinated buying and selling, which destabilizes markets such that hedgers fail to achieve their objective. Gennotte and Leland (1990) show portfolio insurance strategies can have an impact on price movements. Ramanlal and Mann (1996) show how price movements, in turn, can alter hedging strategies. In this paper, we combine these separate effects and develop an equilibrium, executable hedging strategy. This hedging strategy requires less rebalancing than traditional portfolio insurance; more important, it achieves downside protection with a less destabilizing impact on security prices.     

A general equilibrium model of portfolio insurance

This article examines the effects of portfolio insurance onmarket and asset price dynamics in a general equilibrium continuous-timemodel. Portfolio insurers are modeled as expected utility maximizingagents. Martingale methods are employed in solving the individualagents' dynamic consumption-portfolio problems. Comparisonsare made between the optimal consumption processes, optimallyinvested wealth and portfolio strategies of the portfolio insurersand 'normal agents'. At a general equilibrium level, comparisonsacross economies reveal that the market volatility and riskpremium are decreased, and the asset and market price levelsincreased, by the presence of portfolio insurance.     

A risk-neutral equilibrium leading to uncertain volatility pricing

We study the formation of derivative prices in an equilibrium between risk-neutral agents with heterogeneous beliefs about the dynamics of the underlying. Under the condition that short-selling is limited, we prove the existence of a unique equilibrium price and show that it incorporates the speculative value of possibly reselling the derivative. This value typically leads to a bubble; that is, the price exceeds the autonomous valuation of any given agent. Mathematically, the equilibrium price operator is of the same nonlinear form that is obtained in single-agent settings with worst-case aversion against model uncertainty. Thus, our equilibrium leads to a novel interpretation of this price.     

Nonuniform Staggered Prices and Output Persistence

Staggered prices are a fundamental building block of New Keynesian dynamic stochastic general equilibrium models. In the standard model, prices are uniformly staggered, but recent empirical evidence suggests that deviations from uniform staggering are common. This paper analyzes how synchronization of price changes affects the response to monetary policy shocks. I find that even large deviations from uniform staggering have small effects on the response of output. Aggregate dynamics in a model of uniform staggering may serve well as an approximation to a more complicated model with some degree of synchronization in price setting.     

FURTHER EXAMINATION OF PRICE DISCOVERY ON THE NYSE AND REGIONAL EXCHANGES

I re‐examine price discovery on the New York Stock Exchange (NYSE) and regional exchanges. I employ three common‐trend cointegration models to analyze the equilibrium dynamics between the NYSE and regional exchanges for the thirty Dow stocks. The overall results show that whether the regional exchanges free‐ride on the NYSE in obtaining equilibrium prices depends on whether trade prices or quotes are examined. The regional exchanges play a significant (though less important) role in the price‐discovery process for trade prices. However, the contributions of regional exchanges in price discovery of quotes are negligible. I explain the inconsistency between the results using quotes and those using trades. I also highlight the problems of using either quotes or trades in examining this free‐riding hypothesis and suggest future research on the different informativeness of trades on the NYSE and regional exchanges. JEL classification: G20, C32.     

Regulator performance,regulatory environment and outcomes: An examination of insurance regulator career incentives on state insurance markets

In this paper we test whether the past or future labor market choices of insurance commissioners provide incentives for regulators in states with price regulation to either favor or oppose the industry by allowing prices that differ significantly from what would otherwise be the competitive market outcome. Using biographical data on insurance regulators, economic and state specific market structure and regulatory variables, and state premium and loss data on the personal automobile insurance market, we find no evidence consumers in prior approval states paid significantly different “unit prices” for insurance than consumers in states that allow competitive market forces to determine equilibrium prices during the time period 1985–2002. We do, however, find evidence regulators who obtained the position of insurance commissioner by popular election and those who seek higher elective office following their tenure as insurance commissioner allow higher overall “unit prices” relative to competitive market states. The “unit price” of insurance in regulated states is not statistically different from the competitive market outcome for regulators that make lateral moves back into state government and it is mildly higher for regulators who enter the insurance industry following their tenure. Finally, we find some evidence regulators who describe themselves as consumer advocates are successful reducing the price of insurance in favor of consumers in regulated markets. Overall the results are consistent with the existence of asymmetric information in the regulatory process that agents use to enhance their career aspirations.     

Perspectives of Risk Sharing

In this paper we present an overview of the standard risk sharing model of insurance. We discuss and characterize a competitive equilibrium, Pareto optimality, and representative agent pricing, including its implications for insurance premiums. We only touch upon the existence problem of a competitive equilibrium, primarily by presenting several examples. Risk tolerance and aggregation is the subject of one section. Risk adjustment of the probability measure is one topic, as well as the insurance version of the capital asset pricing model. The competitive paradigm may be a little demanding in practice, so we alternatively present a game theoretic view of risk sharing, where solutions end up in the core. Properly interpreted, this may give rise to a range of prices of each risk, often visualized in practice by an ask price and a bid price. The nice aspect of this is that these price ranges can be explained by "first principles", not relying on transaction costs or other frictions. We also include a short discussion of moral hazard in risk sharing between an insurer and a prospective insurance buyer. We end the paper by indicating the implications of our results for a pure stock market. In particular we find it advantageous to discuss the concepts of incomplete markets in this general setting, where it is possible to use results for closed, convex subspaces of an L 2 -space to discuss optimal risk allocation problems in incomplete financial markets.     

What Asset Prices Should Be Targeted by a Central Bank?

This paper investigates the monetary policy design for restoring equilibrium determinacy. Our interests are whether a central bank should respond to asset price fluctuations, and if so, what asset prices should be targeted. We show that a monetary policy response to the price of a productive tangible asset (capital price) is helpful for equilibrium determinacy, while that to the price of an intangible asset that reflects a firm's profit (share prices) is a source of equilibrium indeterminacy. This result comes from the two assets' prices moving in opposite directions in response to a permanent increase in inflation.     

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.     

An open-economy new Keynesian Phillips curve for the U.K.

We estimate a pricing equation or “new Keynesian Phillips curve” (NKPC) obtained from a structural dynamic model of price setting based on Rotemberg [1982. Sticky prices in the United States. Journal of Political Economy 90(6), 1187-1211] and extended to capture employment adjustment costs and the openness of the United Kingdom. This model nests the baseline Galí and Gertler [1999. Inflation dynamics: a structural econometric analysis. Quarterly Journal of Economics 110, 127-159) and Sbordone [2002. Prices and unit labor costs: a new test of price stickiness. Journal of Monetary Economics 49, 265-292] relationship between inflation and marginal cost in the limiting case of no employment adjustment costs, no impact of relative prices of imported inputs on real marginal cost and a constant equilibrium markup. Our findings indicate that each of our modifications to the baseline NKPC model is important for U.K. data, so that inflation in the U.K. is explained both by changes in employment and by changes in real import prices, in general, and real oil prices, in particular. External competitive pressures also seem to affect U.K. inflation via their impact on the equilibrium price markup of domestic firms.     

Can cost increases increase competition? Asymmetric information and equilibrium prices

We present an analysis of competition under asymmetric information where prices react asymmetrically to changes in firms' marginal costs. When one firm has private information about some customers, an increase in an uninformed firm's marginal cost leads to a price increase, as usual. However, an increase in the informed firm's marginal cost causes the equilibrium price to fall by improving the distribution of customers served by the uninformed firm. The model applies to settings where information asymmetries are important determinants of competition, such as credit, insurance, labor markets, or for the sale of goods where repeat business is important.     

A Study of the Interaction of Insurance and Financial Markets: Efficiency and Full Insurance Coverage

The first contribution of this article is to provide a framework, a model together with a corresponding equilibrium notion, suitable for the study of the interaction between insurance and dynamic financial markets. Our central result is that in equilibrium risk‐averse agents purchase full insurance coverage, despite unfair insurance prices. We identify three conditions that explain this result: (1) insurance contracts are priced competitively, (2) financial prices include a risk premium only for undiversifiable risk, and (3) financial markets are effectively complete. An implication is that in this model disasters can be insured by fully assessable stock insurance companies.     

Equilibrium Exhaustible Resource Price Dynamics

We develop equilibrium models of exhaustible resource markets with endogenous extraction choices and prices. Our analysis demonstrates how adjustment costs can generate oil and gas forward price dynamics with two factors, consistent with the behavior these commodities exhibit in the Schwartz and Smith (2000) calibration. Our two‐factor model predicts that stochastic volatility will arise in these markets as a natural consequence of production adjustments, however, and we provide supporting empirical evidence. Differences between endogenous price processes from our general equilibrium model and exogenous processes in earlier papers can generate significant differences in both financial and real option values.     

A general class of distortion operators for pricing contingent claims with applications to CAT bonds

ABSTRACT

The current paper provides a general approach to construct distortion operators that can price financial and insurance risks. Our approach generalizes the (Wang 2000) transform and recovers multiple distortions proposed in the literature as particular cases. This approach enables designing distortions that are consistent with various pricing principles used in finance and insurance such as no-arbitrage models, equilibrium models and actuarial premium calculation principles. Such distortions allow for the incorporation of risk-aversion, distribution features (e.g. skewness and kurtosis) and other considerations that are relevant to price contingent claims. The pricing performance of multiple distortions obtained through our approach is assessed on CAT bonds data. The current paper is the first to provide evidence that jump-diffusion models are appropriate for CAT bonds pricing, and that natural disaster aversion impacts empirical prices. A simpler distortion based on a distribution mixture is finally proposed for CAT bonds pricing to facilitate the implementation.     

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.     

Subsidization and Choice in the Group Health Insurance Market

This study investigates the effect of group health insurance plan choice on insurance unit price. The empirical findings suggest that the unit price of insurance, as measured by the ratio of the premium to expected indemnity benefits, is lower in group plans that offer employees a choice of different insurance options and require a premium contribution than it is in plans lacking at least one of these two features. The analyses suggest that lower unit prices are related to an increase in indemnity benefits and that the reduction in the unit price is greater for lower risks. The findings indicate that although subsidization of high risks by low risks occurs with group health insurance, the degree of subsidization is less when employees are offered a choice of health insurance plans.     

The Effect of Regulation on Insurance Pricing: The Case of Germany

This article analyzes the impact of policy form regulation on the unit price of insurance and determinants of premium changes using the 1994 deregulation of the German property–liability market as a natural experiment. Our result show that policy form regulation did not increase prices above competitive levels. Factors influencing premium changes are significantly different for the two time periods, pre‐ and post‐deregulation, indicating that regulation affects insurance pricing. Focusing on highly competitive lines after deregulation, we find a significant price decrease, and this decrease is offset by higher prices in the remaining other lines.     

Method and tools for insurance price and revenue optimisation

This paper introduces the emerging field of demand-driven insurance price and revenue optimisation. Following an introduction to the field, a case study is presented, illustrating a typical price optimisation project performed on a car comprehensive insurance portfolio at a direct insurance company. The study describes an actual price optimisation process using price testing, demand estimation, margin optimisation and controlled test validation procedures. Demand data were collected from a sample of 10,582 customers during June–July 2002. The subsequent demand-driven price optimisation process generated a profitability impact assessment of 9 per cent in net profit per a 1 per cent loss in customer retention. This assessment was validated in a controlled test conducted on a sample of 12,077 customers who were randomly assigned optimised or non-optimised prices. Test results validated the optimisation assumptions, generating a 10 per cent improvement in expected annual profit.     

Rainfall or Rainmaking? Lawyers,Courts, and the Price of Mold Insurance in Texas

In well‐functioning property‐‐liability insurance markets, the price of coverage reflects the impact of the legal environment on the frequency and severity of claims. This article presents a case study of the Texas mold insurance crisis of 2001–2002. We provide a narrative of the controversy in Texas over insurance coverage for household mold and use county‐level data from a single Texas insurer to assess the determinants of postcrisis prices for supplemental mold, slab, and extended water loss coverages. We find that more attorneys per capita and more heavily Democratic courts were both associated with higher prices for mold and slab coverage.     

Valuation ratios and price deviations from fundamentals

This paper sheds light on US stock price deviations from fundamentals by analyzing the time-series dynamics of post-1870 S&P valuation ratios. It employs a non-linear, two-regime framework that allows for different behavior over phases of the stock market cycle. Persistence in the ratios implies prolonged price deviations from fundamentals stemming from short run continuation fueled by investor sentiment during bull markets. However, the pull from fundamentals ensures that valuation ratios and prices move toward their equilibrium levels in bear markets. Impulse response functions highlight sluggish adjustment and indicate that the effects of positive shocks are more pronounced and long-lasting in bull markets. The main conclusion is that, while market sentiment plays an important transitory role, valuation ratios do mean revert and so prices reflect fundamentals in the long run.