Pricing contingent convertibles: a general framework for application in practice

The first contingent convertibles (CoCo) were issued in 2009, but, to date, the academic community has not given much attention to practical issues of pricing them. Combining various aspects from existing theoretical and practical literature, this paper first presents a CoCo pricing framework that allows a flexible and comprehensible valuation of real-world equity or TIER-1 ratio-triggered CoCos. The model is based on the assumption that the issuer’s total asset value follows a Brownian motion, that book values reflect fair economic values in the case of financial distress, and that there is a linear relationship between straight equity and TIER-1 ratios. The pricing methodology is then applied to the Credit Suisse Buffer Capital Note issued in February 2011.     

Pricing a contingent claim liability with transaction costs using asymptotic analysis for optimal investment

We price a contingent claim liability (claim for short) using a utility indifference argument. We consider an agent with exponential utility, who invests in a stock and a money market account with the goal of maximizing the utility of his investment at the final time T in the presence of a proportional transaction cost ε>0 in two cases: with and without a claim. Using the heuristic computations of Whalley and Wilmott (Math. Finance 7:307–324, 1997), under suitable technical conditions, we provide a rigorous derivation of the asymptotic expansion of the value function in powers of \(\varepsilon^{\frac{1}{3}}\) in both cases with and without a claim. Additionally, using the utility indifference method, we derive the price of the claim at the leading order of \(\varepsilon^{\frac{2}{3}}\) . In both cases, we also obtain a “nearly optimal” strategy, whose expected utility asymptotically matches the leading terms of the value function. We also present an example of how this methodology can be used to price more exotic barrier-type contingent claims.     

Spatial modelling of claim frequency and claim size in non-life insurance

In this paper, models for claim frequency and average claim size in non-life insurance are considered. Both covariates and spatial random effects are included allowing the modelling of a spatial dependency pattern. We assume a Poisson model for the number of claims, while claim size is modelled using a Gamma distribution. However, in contrast to the usual compound Poisson model, we allow for dependencies between claim size and claim frequency. A fully Bayesian approach is followed, parameters are estimated using Markov Chain Monte Carlo (MCMC). The issue of model comparison is thoroughly addressed. Besides the deviance information criterion and the predictive model choice criterion, we suggest the use of proper scoring rules based on the posterior predictive distribution for comparing models. We give an application to a comprehensive data set from a German car insurance company. The inclusion of spatial effects significantly improves the models for both claim frequency and claim size, and also leads to more accurate predictions of the total claim sizes. Further, we detect significant dependencies between the number of claims and claim size. Both spatial and number of claims effects are interpreted and quantified from an actuarial point of view.     

Optimal investment and contingent claim valuation in illiquid markets

This paper extends basic results on arbitrage bounds and attainable claims to illiquid markets and general swap contracts where both claims and premiums may have multiple payout dates. Explicit consideration of swap contracts is essential in illiquid markets where the valuation of swaps cannot be reduced to the valuation of cumulative claims at maturity. We establish the existence of optimal trading strategies and the lower semicontinuity of the optimal value of optimal investment under conditions that extend the no-arbitrage condition in the classical linear market model. All results are derived with the “direct method” without resorting to duality arguments.     

Pricing catastrophe options with stochastic claim arrival intensity in claim time

We model claim arrival and loss uncertainties jointly in a doubly-binomial framework to price an Asian-style catastrophe (CAT) option with a non-traded underlying loss index using the no-arbitrage martingale pricing methodology. We span these uncertainties by benchmarking to the shadow price of a one-claim bond and the premium of a reinsurance contract. We implement a stochastic time change from calendar time to claim time to more efficiently price the CAT option as a random sum – a binomial sum of claim time binomial Asian option prices. This choice of the operational time dimension allows us to incorporate different patterns of catastrophe arrivals by adjusting the claim arrival probability. We demonstrate this versatility by incorporating a mean-reverting Ornstein-Uhlenbeck intensity arrival process. Simulation results verify our model predictions and demonstrate how the claim arrival probability varies with the expected claim arrival intensity.     

英国新建宏观审慎的金融监管框架及启示

英国金融体系未能幸免于2008年国际金融危机的冲击,暴露出英国金融监管框架同样存在明显缺陷。为此,英国政府决心对其金融监管框架进行改革,将基于系统整体的宏观审慎监管与传统的基于单个金融机构的微观审慎监管结合起来。文章介绍了英国监管当局对其旧监管体系的反思,及新监管框架的结构与运行模式,并在此基础上总结了当前国际金融业监管新趋势对我国的启示。     

Life insurance companies as investment managers: New implications for consumers

This paper examines the attractiveness of the equity portfolios of life insurance companies as an alternative investment to mutual funds. In particular, this study analyzes the risk-adjusted investment performance of the stock portfolios of life insurance companies, attributable to their stock selection and market timing abilities. Using conventional measures of risk-adjusted portfolio performance, we find that life insurance companies exhibit performance similar to mutual funds. The evidence suggests that the life insurance companies, like their mutual fund counterparts, fail to exhibit differential stock selection or market timing abilities that are statistically significant. While the risk-adjusted investment performance of the two investment vehicles is similar, the variable annuity contracts of life insurance companies may offer an edge over mutual funds due to their ability to defer taxes.     

Convex duality in optimal investment and contingent claim valuation in illiquid markets

This paper develops duality theory for optimal investment and contingent claim valuation in markets where traded assets may be subject to nonlinear trading costs and portfolio constraints. Under fairly general conditions, the dual expressions decompose into three terms, corresponding to the agent’s risk preferences, trading costs and portfolio constraints, respectively. The dual representations are shown to be valid when the market model satisfies an appropriate generalization of the no-arbitrage condition and the agent’s utility function satisfies an appropriate generalization of asymptotic elasticity conditions. When applied to classical liquid market models or models with bid–ask spreads, we recover well-known pricing formulas in terms of martingale measures and consistent price systems. Building on the general theory of convex stochastic optimization, we also obtain optimality conditions in terms of an extended notion of a “shadow price”. The results are illustrated by establishing the existence of solutions and optimality conditions for the nonlinear market models recently proposed in the literature. Our results allow significant extensions including nondifferentiable trading costs which arise, e.g., in modern limit order markets where the marginal price curve is necessarily discontinuous.     

Pricing insurance and warranties: Ambiguity and correlated risks

This paper reports on the results of a questionnaire study of pricing decisions made by professional actuaries when the probabilities of a loss are either ambiguous or nonambiguous. Theoretical hypotheses derived from the expected utility model were compared with the implications of procedures described by practicing actuaries. Actuaries were asked to act as consultants to a computer manufacturer concerning the price of a warranty. The suggested prices were considerably higher when probabilities were ambiguous than when they were well-specified. These pricing decisions were consistent with the procedures described by actuaries but inconsistent with predictions from expected utility theory when the risks are perfectly correlated. Further insight into the actual decision process is provided by interviews with actuaries and an analysis of comments written on the questionnaire forms.     

临时保险制度：赔付理由、期间及其限制

我国《保险法》未规定临时保险制度,本文建议,我国的临时保险制度应当分为强制临时保险与自愿临时保险两种,在保险人预收保险费的情况下,根据履行提前、对价平衡、合理期待等理论,保险人应当对临时保险事故予以赔付,此种临时保险的期间自投保人交付保险费之时起算,于正式保险生效之时或投保人收到拒保通知书并由保险人退还保险费之时终止;...     

Asymmetric information in insurance: general testable implications

Several recent articles on empirical contract theory and insurance have tested for a positive correlation between coverage and ex post risk, as predicted by standard models of pure adverse selection or pure moral hazard. We show here that the positive correlationproperty can be extended to general setups: competitive insurance markets and cases where risk aversion is public. We test our results on a French dataset. Our tests confirm that the estimated correlation is positive; they also suggest the presence of market power.     

Alternative forms of deposit insurance: Pricing and bank incentive issues

This paper derives formulas for a deposit insuring agency's liability (and hence a fair value deposit insurance premium) and the equilibrium value of bank equity, considering a wide variety of factors affecting individual bank risk. Both fixed rate and variable rate (risk-sensitive) insurance systems are analyzed. Consideration is made as to whether the deposit insuring agency makes direct payments to depositors or arranges mergers following bank closings. The effect of these various policy choices on banks' incentive for risk taking is also analyzed.     

A hierarchical model for the estimation of claim rates in a motor car insurance portfolio

Abstract

The present paper gives practical examples involving motor car insurance portfolios which we believe provide a natural setting in which collateral data should be used. In passing, the problem of assigning partial credibility is solved and an application of the empirical linearized Bayes estimators to experience rating is discussed.     

Pricing and hedging contingent claims using variance and higher order moment swaps

This paper suggests perfect hedging strategies of contingent claims under stochastic volatility and random jumps of the underlying asset price. This is done by enlarging the market with appropriate swaps whose pay-offs depend on higher order sample moments of the asset price process. Using European options and variance swaps, as well as barrier options written on the S&P 500 index, the paper provides clear cut evidence that hedging strategies employing variance and higher order moment swaps considerably improves upon the performance of traditional delta hedging strategies. Inclusion of the third-order moment swap improves upon the performance of variance swap-based strategies to hedge against random jumps. This result is more profound for short-term out-of-the money put options.     

Pricing catastrophe risk in life (re)insurance

What is the catastrophe risk a life insurance company faces? What is the correct price of a catastrophe cover? During a review of the current standard model, due to Strickler, we found that this model has some serious shortcomings. We therefore present a new model for the pricing of catastrophe excess of loss cover (Cat XL). The new model for annual claim cost C is based on a compound Poisson process of catastrophe costs. To evaluate the distribution of the cost of each catastrophe, we use the Peaks Over Threshold model for the total number of lost lives in each catastrophe and the beta binomial model for the proportion of these corresponding to customers of the insurance company. To be able to estimate the parameters of the model, international and Swedish data were collected and compiled, listing accidents claiming at least twenty and four lives, respectively. Fitting the new model to data, we find the fit to be good. Finally we give the price of a Cat XL contract and perform a sensitivity analysis of how some of the parameters affect the expected value and standard deviation of the cost and thus the price.     

Life insurance demand and borrowing constraints

The literature devoted limited attention to exploring the relationship between financial development and life insurance demand. Financial development supports life insurance supply by providing confidence in the financial system, more efficient payment systems, and higher availability of financial instruments. However, financial development reduces households' needs to save by relaxing borrowing constraints, indirectly affecting life insurance demand. We contribute by providing a demand‐driven explanation of the negative consequences of financial development on life insurance development. We find that more credit‐constrained countries have higher life insurance penetration on average. Indirectly, the role of borrowing constraints signifies the importance of life insurance policies as a financing tool in case of the realization of various background risks. This study integrates the knowledge from life insurance theory, life insurance lapse, policy loans demand, and saving under liquidity constraints literature and produces implications for researchers, policymakers, and life insurers.     

财险公司未决赔款准备金波动风险及其防范对策

未决赔款准备金作为财险公司最大的负债项目之一,通过不断提高数据的真实性与有效性,加强未决赔款准备金的波动风险的管理,有利于我国财险公司与财险行业的稳健经营与持续发展。未决赔款准备金波动风险产生的主要原因有数据的可靠性、精算评估方法的波动性以及宏观管理因素与经营环境的变化。通过切实提高管理水平、提升公司的精算技术、加强精细化经营理念的宣导以及加强非寿险行业的精算标准建设,将能有效地防范未决赔款准备金波动风险。