One Approach to Dual Randomness in Life Insurance

Abstract

1. The Unnatural Hypothesis of a Constant Rate of Interest

There are loan contracts which assume a constant interest during several years and thereafter payment of the amount borrowed, but nowadays clauses are as a rule admitted giving the debtor right of conversion or repayment after a certain period, generally ten years. Low interest loans can be considered as perpetuities from a practical point of view, as long as no possibility is meant to exist that the market rate will fall under their nominal rate. Such a loan—as e.g. Consols—with the nominal rate i ₀ ought to be valued at a discount if the market rate is higher, say i > i ₀, the value being equal to the fraction i ₀ : i. But constant rates are no rule in practice.     

V. E. Gamborg

Abstract

A glance at the numerous papers dealing with the influence of the rate of interest on the value of premiums will show that most authors aim at computing annuity values for a new rate of interest without first re-calculating the commutation columns, It is only in exceptional cases that they derive premiums or policy-values directly, i.e. without first finding annuity values.² Apart from the fact, that both premiums and policyvalues are implicitly given by a set of annuity values, the reason for the usual procedure lies in the type of calculations which is contemplated, since they cannot conveniently be applied to such ratios as premiums and policy-values. In the following lines we show how the method developed by A. J. Lotka ³ for the calculation of the rate of increase of a stable population is capable of generalisation and of successful application to our problem; thus the detour via the calculation of annuity values can be avoided.     

Voluntary Termination of Life Insurance Policies

Abstract

In this paper, one error-correction model (ECM) that is able to avoid the problem of producing noise within traditional multiple cointegration vectors has been employed to explore the dynamics of surrender behavior. The evidence shows that both the emergency fund hypothesis and interest rate hypothesis are sustained in the short run as well as in the long run. A unique cointegration relationship within the surrender dynamics has been validated. In addition, a new hypothesis test that stresses the competition for the withdrawal of life insurance policy cash values has also been conducted. Such a crowding-out effect between policy loans and policy surrenders might be attributed to the motivation that keeps a life policy in force, the existence of surrender charges, and the automatic premium loan provision.     

Efficient Stochastic Modeling for Large and Consolidated Insurance Business: Interest Rate Sampling Algorithms

Abstract

One of the challenges of stochastic asset/liability modeling for large insurance businesses is the run time. Using a complete stochastic asset/liability model to analyze a large block of business is often too time consuming to be practical. In practice, the compromises made are reducing the number of runs or grouping assets into asset categories. This paper focuses on the strategies that enable efficient stochastic modeling for large and consolidated insurance business blocks. Efficient stochastic modeling can be achieved by applying effective interest rate sampling algorithms that are presented in this paper. The algorithms were tested on a simplified asset/liability model ASEM (Chueh 1999) as well as a commercial asset/liability model using assets and liabilities of the Aetna Insurance Company of America (AICA), a subsidiary of Aetna Financial Services. Another methodology using the New York 7 scenarios is proposed and could become an enhancement to the Model Regulation on cash flow testing, thus requiring all companies to do stochastic cash flow testing in a uniform, nononerous manner.     

Optimal Dividends In An Ornstein-Uhlenbeck Type Model With Credit And Debit Interest

Abstract

In the absence of investment and dividend payments, the surplus is modeled by a Brownian motion. But now assume that the surplus earns investment income at a constant rate of credit interest. Dividends are paid to the shareholders according to a barrier strategy. It is shown how the expected discounted value of the dividends and the optimal dividend barrier can be calculated; Kummer’s confluent hypergeometric differential equation plays a key role in this context. An alternative assumption is that business can go on after ruin, as long as it is profitable. When the surplus is negative, a higher rate of debit interest is applied. Several numerical examples document the influence of the parameters on the optimal dividend strategy.     

The value of relationship banking: International evidence

This paper analyses whether repeated borrowing from the same bank affects loan contract terms. We find that relationship loans pay less spread and require less collateral compared to non-relationship loans. These effects for relationship loans are not derived from differences between relationship and nonrelationship loans. The reduction of interest rate spread for relationship loans disappeared during the financial crisis. The results also reveal that borrowers paid higher interest rate spreads, had to post more collateral and the maturity was shortened during the crisis period. The reduction in interest rate spread and collateral depends on the protection of creditors’ rights. In countries where creditors’ rights are well protected, relationship loans pay less spread and are required to post less collateral than relationship loans in countries with weak protection of creditors’ rights.     

The economic role of foreclosures

We consider the economic consequences of changing the foreclosure rules. By incorporating renegotiation into the analysis, we show that although renegotiation decreases the number of foreclosures it can make the effects of foreclosure more significant. Even when foreclosure does not actually occur, a change in foreclosure rules changes the threat points of lender and borrower in any renegotiation, and thus changes the effective interest rate that the lender receives. In the long run, stated interest rates on loans will adjust to compensate for any change in the effective interest rate. We also examine the impact of a change in foreclosure laws on the borrower's welfare.     

Hedging Longevity Risk When Interest Rates are Uncertain

Abstract

This paper proposes an asset liability management strategy to hedge the aggregate risk of annuity providers under the assumption that both the interest rate and mortality rate are stochastic. We assume that annuity providers can invest in longevity bonds, long-term coupon bonds, and shortterm zero-coupon bonds to immunize themselves from the risks of the annuity for the equity holders subject to a required profit. We demonstrate that the optimal allocation strategy can lead to the lowest risk under different yield curves and mortality rate assumptions. The longevity bond can also be regarded as an effective hedging vehicle that significantly reduces the aggregate risk of the annuity providers.     

Banks’ Governance and Innovation: Evidence from the Listed Firms in China

ABSTRACT

The article investigates the relationship between banks, agency costs, and innovation ability of listed firms. The role of banks in affecting innovation is a very important topic especially in China where banks play more important roles than equity markets. We find that banks providing short-term funds to listed non-high-tech firms dampen their innovation ability significantly. However, the relationship between short-term loans and innovation ability in high-tech firms is insignificant. The effects of short-term loans on innovation ability are significantly different between high-tech and non-high-tech firms. Further examination shows that high-tech firms with more short-term bank loans have significantly less abnormal management expenses than non-high-tech firms in the next year. The reduced abnormal management expenses in the next year significantly enhance the innovation ability in the year after next.     

Valuation of Mortgage Servicing Rights with Foreclosure Delay and Forbearance Allowed

We develop a bivariate binomial model to price Mortgage Servicing Rights (MSRs). Our model is an improvement over previous MSR pricing models by explicitly incorporating the realistic assumptions that there are additional costs involved in servicing delinquent loans. In addition to the Hilliard et al. mortgage-pricing tree, we extend additional sub-branches to model the borrower's decision of prepayment, cure, and foreclosure after a loan becomes delinquent. We then investigate how the value of the Mortgage Servicing Right varies with interest rate volatility, house price volatility, delinquency options, deficiency judgments, default penalties, forbearance periods, and speed of adjustments factors. JEL Classification: C15, G21     

Banks' option to lend,interest rate sensitivity,and credit availability

Interest rate risk is a major concern for banks because of the nominal nature of their assets and the asset-liability maturity mismatch. This paper proposes a new way to derive a bank's interest rate sensitivity, by examining separately the effects of interest rate changes on existing loans(loans-in-place) and potential loans (loans-in-process). A potential loan is shown to be equivalent to an American option to lend, and is valued using option theory. An increase in interest rates generally has a negative effect on existing loans. However, if both deposit and lending rates rise by the same amount, the value of a potential loan generally increases. Hence a bank's lending slack (or ratio of loans-in-process to loans-in-place) will determine its overall interest rate risk. Empirical evidence indicates that low-slack banks indeed have significantly more interest rate risk than high-slack banks. The model also makes predictions regarding the effect of deposit and lending rate parameters on bank credit availability. Empirical tests with quarterly data are generally supportive of these predictions. This revised version was published online in June 2006 with corrections to the Cover Date.     

The Risk‐Taking Channel of Monetary Policy: Exploring All Avenues

The literature on the risk‐taking channel of monetary policy grew quickly, leading to scattered evidence. We examine this channel through different angles, exploring detailed information on loan origination and performance. Ex ante riskier borrowers receive more funding at the extensive margin when interest rates are lower. Ex post performance is independent of the level of interest rates at origination. Still, loans granted in periods of very low and stable interest rates show higher default rates once interest rates start to increase. Risk‐taking is stronger among banks with lower capital ratios, suggesting that this channel may be linked to managerial incentives for risk‐shifting.     

Generic pricing of FX,inflation and stock options under stochastic interest rates and stochastic volatility

We consider the pricing of FX, inflation and stock options under stochastic interest rates and stochastic volatility, for which we use a generic multi-currency framework. We allow for a general correlation structure between the drivers of the volatility, the inflation index, the domestic (nominal) and the foreign (real) rates. Having the flexibility to correlate the underlying FX/inflation/stock index with both stochastic volatility and stochastic interest rates yields a realistic model that is of practical importance for the pricing and hedging of options with a long-term exposure. We derive explicit valuation formulas for various securities, such as vanilla call/put options, forward starting options, inflation-indexed swaps and inflation caps/floors. These vanilla derivatives can be valued in closed form under Schöbel and Zhu [Eur. Finance Rev., 1999, 4, 23–46] stochastic volatility, whereas we devise an (Monte Carlo) approximation in the form of a very effective control variate for the general Heston [Rev. Financial Stud., 1993, 6, 327–343] model. Finally, we investigate the quality of this approximation numerically and consider a calibration example to FX and inflation market data.     

On stock-based loans

We investigate the equilibrium interest rate charges on non-recourse and recourse loans secured by stock. In such loans, the client retains the option to prepay and recover the collateral stock. We adopt a structural model of the firm where debt levels, with endogenous bankruptcy, affect equity dynamics. Complicating matters, the link between total equity and the price of a share of stock that forms the collateral depends on the extent of dilutions and buybacks that occur. For levered firms, due to dilution in bad states of nature, stock prices typically fall faster than equity values; and for firms that engage in buybacks in good states of nature, stock prices will rise faster than equity values. Banks that ignore these features underestimate the equilibrium interest rate charge on stock-based loans. We provide an analysis of individual stock-based loans and their portfolio characteristics, the latter of which can be used by banks to ascertain capital requirements.     

利率市场化对农户投资行为影响的实证分析

1998-2004年,农村信用社存贷款利率浮动区间不断扩大,在垄断的农村金融市场结构下,农村金融机构有将贷款利率上浮到顶的内在冲动,贷款利率的上浮是否会超出农户承受力,影响到农业生产.本文拟围绕农产品利润率展开分析,以农业贷款利率小于或等于农产品利润率作为影响农户投资行为的主要依据.研究发现,近年来,农业平均利润率约在20%左右,可以承受贷款利率浮动上限,利率市场化增强了农户贷款可得性.     

Multiperiod Loans,Occasionally Binding Constraints,and Monetary Policy: A Quantitative Evaluation

We introduce multiperiod mortgage loans, fixed interest rate, a lower bound constraint on newly granted loans, and a possibly slack collateral constraint, in an otherwise standard Dynamic Stochastic General Equilibrium (DSGE) model with housing. Our nonlinear estimation shows that all those features are important to understand the evolution of mortgage debt during the recent U.S. housing market boom and bust. The transmission of monetary policy becomes dependent on the housing cycle, with weaker effects when house prices are high or start falling sharply. Higher average loan duration makes monetary policy less effective, eventually leading to asymmetric responses to positive and negative monetary shocks.     

Trade-off Model of Debt Maturity Structure

In this paper, we suggest the trade-off model to explain the choice of debt maturity. This model is based on balancing between risk and reward of using shorter-term loans. Shorter-term loans have cost advantage over, but incur higher refinancing and interest rate risk than longer-term loans. Using the Compustat data, we show that the principal components of financial attributes are financial flexibility and financial strength. Therefore, only firms with greater financial flexibility and financial strength can use proportionately more short-term loans. We also document that financially strong firms take advantage of lower interest rates of short-term debt. They use proportionately more short-term loans when the term premium is high. The results of our study also provide evidence supporting the agency cost hypothesis, which is strongly supported by current literature.     

A Technique for Reducing Discretization Bias from Monte Carlo Simulations: Option Pricing under Stochastic Interest Rates

Abstract

Control variates are often used to reduce variability in Monte Carlo estimates and their effectiveness is traditionally measured by the so-called speed-up factor. The main objective of this paper is to demonstrate that a control variate can also be applied to reduce the bias stemming from the discretization of the state variable dynamics. This is particularly valuable when stochastic interest rate models are discretized, since bias reduction through more grid points is computationally expensive.     

2010年1～9月国内金融形势评述

2010年前三季度,货币信贷市场平稳运行,金融体系持续稳定健康。主要特点是：货币增速总体呈回落态势;人民币贷款投放平稳,中长期贷款需求保持旺盛;企业存款和储蓄存款增速由降转升;银行间市场交易活跃,市场利率总体有所回升;人民币汇率弹性增强,9月末海外市场对人民币升值预期比上年末有所减弱。