On a rank-order test for the equality of probability of an event

Abstract

The following situation is considered. A fixed number (= n) or sequence of independent trials T ₁ T ₂,…, T _n is given, and in each of these an event E mayor may not occur, It is further observed that the event E occurs a total of k times amongst the n trials T _i , (i = l,…, n). It is then required to test the hypothesis H ₀ that the probability of the occurrence of E is constant from trial to trial, i.e. H ₀ is the hypothesis: p ₁ = p ₂ = ? = p _n = p, if p _n (i = 1, …, n) represents the probability that E occurs on the ith trial.     

操作目标利率的选择与传导 ——基于MLF利率与隔夜利率的实证检验

依据2014-2018年月度数据,运用VAR模型考量MLF利率与隔夜利率对贷款加权利率、商业银行行为以及金融市场利率与金融市场波动的影响.结果表明:MLF利率对贷款加权利率和商业银行行为的影响较大,隔夜利率对金融市场利率和金融市场波动的影响较大.鉴此,应利用MLF利率调节贷款加权利率与商业银行行为,利用隔夜利率调节金融市场利率与金融市场波动,当两种利率的调节效果收敛接近时,再最终确定唯一的操作目标利率.     

Optimal Loan Interest Rate Contract Design

This paper analyzes optimal loan interest rate contracts under conditions of risky, symmetric information for one-period (static) and multi-period (dynamic) models. The optimal loan interest rate depends upon the volatility of, and co-variation among the market interest rate, borrower collateral, and borrower income, as well as the time horizon and the risk preferences of lenders and borrowers. For a risk-averse borrower with stochastic collateral, variable interest rate contracts are, in general, Pareto optimal. For plausible assumptions, the optimal loan interest rate for the multi-period model often exhibits muted responses to changes in market interest rates, making fixed rate loans a reasonable approximation for the optimal loan. Hence, in the absence of optimal contracts, long-term (short-term) borrowers tend to prefer fixed rate (variable) contracts.     

Risk theory in a Markovian environment

Abstract

We consider risk processes _{t t?0} with the property that the rate β of the Poisson arrival process and the distribution of B of the claim sizes are not fixed in time but depend on the state of an underlying Markov jump process {Z_t } _t?0 such that β=β _i and B=B_i when Z_t=i . A variety of methods, including approximations, simulation and numerical methods, for assessing the values of the ruin probabilities are studied and in particular we look at the Cramér-Lundberg approximation and diffusion approximations with correction terms. The mathematical framework is Markov-modulated random walks in discrete and continuous time, and in particular Wiener-Hopf factorisation problems and conjugate distributions (Esscher transforms) are involved.     

利率上浮及其与贷款基准利率的关系探究

对31个省市2005-2015年的1~3年期贷款利率上浮幅度进行测算,并通过统计分析与面板模型对其与贷款基准利率的关系进行探索性研究,结果显示:贷款利率上浮幅度与贷款基准利率负相关,贷款利率上浮幅度自2010年开始快速上升;不同地区的上浮幅度差异大,存在明显的区域异质性,中国人民银行通过基准利率调整进行宏观调控时,主要对北京市、上海市的贷款利率形成传递效应,对其它地区的影响相对较小;且随着时间的推移,基准利率政策的有效性越来越低.因此,为发挥基准利率政策的有效性,应在适度区间进行基准利率调节,加强中国人民银行对地方性商业银行的宏观审慎管理能力,同时与数量型货币政策相配合.     

A Generalization of the Formulas for Options on the Maximum or the Minimum of Several Assets

Abstract

This paper generalizes the option on the maximum or the minimum of two assets (several assets) within a stochastic interest rate framework. A Gaussian model is used to describe the interest rates. Closed-form solutions for the market values are presented. The use of the options is illustrated with numerical examples.     

关于我国利率和利率传导关系的思考

当前我国银行体系利率大致可分为货币市场利率和信贷市场利率,其中由央行指定的利率主要有存贷款基准利率、再贴现率等。在货币市场上,隔夜同业拆借利率具有基准利率的地位。在信贷市场上,在特定时期,保持适当的存贷款利差具有积极意义。由于一些阻碍信贷市场与货币市场统一的制度安排的存在,这两个市场间的利率传导呈现出一定的不对称性。为推进利率市场化,进一步完善我国利率体系,下一步应逐步弥合市场分割,加强货币市场基准利率建设,培育商业银行利率定价能力。     

The effect of the interest coverage covenants on classification shifting of revenues

ABSTRACT

While prior studies focus on real/accrual-based earnings management and expense misclassification to investigate earnings manipulation in avoiding covenant violations, this paper extends such research in a new direction. In particular, it examines whether firms employ classification shifting of revenues when they are subject to interest coverage EBITDA-based covenants close to their threshold values or limits. This earnings management tool allows firms to increase reported EBITDA by misclassifying non-operating revenues as operating revenues to remain within covenant limits that include EBITDA. Using a sample of 559 UK listed firm-years for the period 2005–2014, it establishes that the use of classification shifting of revenues is high when interest coverage covenants are close to their limits. Further analysis suggests that firms also employ revenue shifting when all their loan covenants are EBITDA-related.     

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.     

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.     

An index of market shocks based on multiscale analysis*

Abstract

Financial markets are places of sudden and violent price movements. Nevertheless, financial crises lack a universally recognized way of assessing their gravity. This has motivated the measure recently proposed and applied to the exchange rates market by Zumbach et al (2000a Int. J. Theor. Appl. Finance 3 347–55). This measure relies on an analogy with geophysics: the scale of market shocks (SMS) is equivalent to the Richter scale used for earthquakes. More precisely, as a market is the place where economic agents—with different investment horizons—interact, the SMS definition is a weighted aggregation of volatility measures corresponding to these different horizons. In this paper, we implement and apply a similar measure to stock markets, and adapt it to take into account some extra features of these markets.

The volatilities are first described, and then used to assess the market instability perceived by a market participant. The evolution of our index of market shocks (IMS)—after rescaling for easy interpretation—is presented using different computational methods.

The IMS is then compared with another multiscale measure, the multifractal spectrum width, and we also investigate the links between the IMS and the daily close-to-close returns and volatility. Finally, we describe the recent turbulence on the French market using the IMS as an exploratory tool, concluding that the events of September 2001 proved to be a major shock compared to the Russian and Asian crises.     

The nominal duration of TIPS bonds

This paper studies the price responsiveness (effective duration) of U.S. government issued inflation-indexed bonds, known by the acronym TIPS (Treasury Inflation-Protected Securities), to changes in nominal interest rates, real interest rates, and expected inflation. Using the TIPS pricing formula derived by Laatsch and Klein [Q. Rev. Econ. Finance 43 (2002) 405], we first confirm that TIPS bonds have zero sensitivity to changes solely in expected inflation. By changes solely in expected inflation, we mean that the real rate remains unchanged and the nominal rate changes in accordance with the established Fisher [Publ. Am. Econ. Assoc. 11 (1896)] effect. We show that the first derivative of the TIPS price is zero whenever the real rate is held constant. Thus, the first partial derivative of the TIPS bond pricing formula with respect to expected inflation is zero and the first partial derivative of the TIPS bond price with respect to nominal rates is also zero, given, in each case, that we hold the real rate constant. We then temporarily shift the analysis to zero-coupon TIPS bonds and zero-coupon ordinary Treasury bonds. We prove that the nominal duration of zero-coupon TIPS bonds equals that of zero-coupon ordinary Treasury bonds when the real rate changes but expected inflation is held constant.However, if expected inflation changes and the change in the nominal rate does not yield a constant real rate, zero-coupon TIPS prices will change and they will change by a smaller percentage than will zero-coupon ordinary Treasury bonds. We analyze TIPS responsiveness to changes in nominal rates under such conditions. We derive an approximation to effective duration that demonstrates that the effective durations of various maturity zero-coupon TIPS bonds are approximately linear functions in time to maturity of the effective duration of the one-year zero-coupon TIPS bond, ceteris paribus.Nominal effective duration of TIPS bonds is certainly of interest to fixed income portfolio managers that might have a desire to include such bonds in their portfolio. After all, the greater portion of a typical fixed income portfolio is in traditional, noninflation protected bonds whose major risk exposure is to changes in nominal rates. To properly assess the role of TIPS bonds in the portfolio, portfolio managers need information as to how TIPS bonds respond to the changes in nominal rates that are driving the price behavior of the bulk of the portfolio's assets. Prior to concluding the paper, we demonstrate how portfolio managers can calculate the nominal durations of coupon TIPS bonds using the zero-coupon duration formula we derive.     

On the analysis of a multi-threshold Markovian risk model

We consider a class of Markovian risk models perturbed by a multiple threshold dividend strategy in which the insurer collects premiums at rate c _i whenever the surplus level resides in the i-th surplus layer, i=1, 2, …,n+1 where n<∞. We derive the Laplace-Stieltjes transform (LST) of the distribution of the time to ruin as well as the discounted joint density of the surplus prior to ruin and the deficit at ruin. By interpreting that the insurer, whose gross premium rate is c, pays dividends continuously at rate d _i =c?c _i whenever the surplus level resides in the i-th surplus layer, we also derive the expected discounted value of total dividend payments made prior to ruin. Our results are obtained via a recursive approach which makes use of an existing connection, linking an insurer's surplus process to an embedded fluid flow process.     

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.     

A positive interest rate model with sticky barrier

This paper proposes an efficient model for the term structure of interest rates when the interest rate takes very small values. We make the following choices: (i) we model the short-term interest rate, (ii) we assume that once the interest rate reaches zero, it stays there and we have to wait for a random time until the rate is reinitialized to a (possibly random) strictly positive value. This setting ensures that all term rates are strictly positive.

Our objective is to provide a simple method to price zero-coupon bonds. A basic statistical study of the data at hand indeed suggests a switch to a different mode of behaviour when we get to a low level of interest rates. We introduce a variable for the time already spent at 0 (during the last stay) and derive the pricing equation for the bond. We then solve this partial integro-differential equation (PIDE) on its entire domain using a finite difference method (Cranck–Nicholson scheme), a method of characteristics and a fixed point algorithm. Resulting yield curves can exhibit many different shapes, including the S shape observed on the recent Japanese market.     

A model for credit rationing by international banks

The theory of credit rationing asserts that commercial banks tend to underprice the nominal interest rate and, in addition, adjust other factors of the loan contract. These various risk adjusters constitute a `price vector'. A model is provided which demonstrates discrete tradeoffs between the interest rate and non-price adjusters such as loan size, maturity, compensating balances, and up-front loan fees. The model utilizes a modification of the asset pricing model to adjust for loan size. In addition, it observes the term structure of interest rates to develop a method of converting interest rates to years of maturity. Derivations are provided for adjustments in compensating balances and loan fees. A simulation is shown to demonstrate the operationalization of the model for international commercial banks lending to foreign government-guaranteed corporations.     

我国利率市场化的目标、障碍和对策探讨

利率市场化的实现表现在两个层面上:一是在宏观层面上,表现为借贷市场资金的供求均衡决定利率总水平;二是在微观层面上,表现为具体融资项目的当事人根据项目的特点,通过协商或讨价还价,自主决定融资项目的利率.目前,我国整个利率体系的基准利率确定困难、商业银行风险定价能力不足以及利率市场化之后可能出现的存贷利差缩小是推进利率市场化进程的主要障碍.本文认为:我们应根据现有市场条件构建基准利率指标,为各具特点的融资项目提供合理的定价基础;商业银行应在市场建设的同时积极实践,以提高风险定价能力;商业银行之间应避免过度竞争,以保持合理利差.     

A Statistical Method for Monitoring a Change in the Rate of Nonacceptable Inpatient Claims

Abstract

This paper is an extension of earlier work (Rosenberg 1998; Rosenberg, Andrews, and Lenk 1999; Rosenberg and Griffith 2000) that introduced a statistical control model to supplement current efforts inexpensively to help reduce unnecessary expenditures. The application of the study was to predict the rate of nonacceptable inpatient claims (NACs). In that work, a statistical model was proposed to link information obtained through an expensive audit with inexpensive information that is readily available to estimate the probability that a claim is a NAC. The premise was that a statistical system can be developed to supplement the expensive audit for additional control between audits.

Estimates of the NAC rate obtained from the statistical model are used as input in a statistical monitor to assess whether the NAC rate had changed over time. The statistical monitor is the subject of this paper. The idea is that subgroups of claims can be analyzed inexpensively with the statistical monitor to determine whether any current intervention is required prior to the time of the next scheduled audit, or whether adjustments are needed in the determination of claims to be sampled for the audit. In this study, the estimate for the NAC rate at t ₀ is compared against the estimate of the NAC rate at some later time t ₁. A decision rule is proposed to assess whether a change in the NAC rate has occurred for that subgroup. The methodology is also applicable to other health care measurements.