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.     

The performance of insolvency prediction and credit risk models in the UK: A comparative study

Theoretically-driven, market-based contingent claims models have recently been applied to the field of corporate insolvency prediction in an attempt to provide the art with a theoretical methodology that has been lacking in the past. Limited studies have been carried out in order directly to compare the performance of these models with that of their accounting number-based counterparts. We use receiver operating characteristic curves to assess the efficacy of thirteen selected models using, for the first time, post-IFRS UK data; and investigate the distributional properties of model efficacy. We find that the efficacy of the models is generally less than that reported in the prior literature; but that the contingent claims models outperform models which use accounting numbers. We also obtain the counter-intuitive finding that predictions based on a single variable can be as efficient as those which are based on models which are far more complicated – in terms of variable variety and mathematical construction. Finally, we develop and test a naïve version of the down-and-out-call barrier option model for insolvency prediction and find that, despite its simple formulation, it performs favourably compared alongside other contingent claims models.     

基于随机微分博弈的保险公司最优决策模型

本文研究了基于保险公司与自然之间二人-零和随机微分博弈的最优投资及再保险问题。假设保险公司具有指数效用,自然是博弈的虚拟对手,通过求解最优控制问题对应的HJB I方程,得到了保险公司的最优投资和再保险策略以及最优值函数的闭式解。结果显示,在完全分保时(即自留比例为零),保险公司应该将全部财富购买无风险资产,即风险资产投资额为零;在不完全分保时保险公司将卖空风险资产,且卖空数量及保险自留比例都随保险公司盈余过程与风险资产间的相关性的提高而增大,随终止时刻T的临近而增加,但随市场中无风险资产回报率的增加而减少。     

A rating model for loss of profits insurance

Abstract

In this paper we present a rating model for loss of profits insurance for a production system consisting of n production units. Explicit expressions for the company's long run expected average claims expenditures are derived. A numerical example is given.     

Risk based capital for guaranteed minimum withdrawal benefit

The guaranteed minimum withdrawal benefit (GMWB), which is sold as a rider to variable annuity contracts, guarantees the return of total purchase payment regardless of the performance of the underlying investment funds. The valuation of GMWB has been extensively covered in the previous literature, but a more challenging problem is the computation of the risk based capital for risk management and regulatory reasons. One needs to find the tail distribution of the profit–loss function, which differs from its expected payoff required for pricing the GMWB contract. GMWB has embedded two option-like features: Management fees are proportional to the current value of the policyholder’s account which results in an average price of the account. Thus the contract resembles an Asian option. However, the fees are charged only up to the time of the account hitting zero which resembles a barrier option payoff. Thus the GMWB is mathematically more complicated than Asian or barrier options traded on the financial markets. To the authors’ best knowledge, this is the first paper in the literature to formulate and analyse profit–loss distribution using PDE methods of such a product with intricate option-like features. Our approach is much more efficient than the current market practice of rather intensive and expensive Monte Carlo simulations due to the lack of samples for extreme cases.     

A Study of Mutual Insurance for Bank Deposits

This article displays a study on the mutual insurance of bank deposits. A system where deposits are first insured by a consortium then by the Government is envisaged. We wish to compute the fair premia due to both the consortium and the Government. Various types of covenants aiming at making banks reduce their risks are detailed. These provisions can be, as is the case in Chapter 11, of a Parisian type. This means that surveillance is based on the path followed by the assets or the leverage. We compare these various types of covenants and conclude on the proposal for new regulatory provisions. JEL Classification No: G13, G21     

A note on different models of stochastic processes dealt with in the collective theory of risk

Abstract

1. For the definition of general processes with special regard to those concerned in Collective Risk Theory reference is made to Cramér (Collective Risk Theory, Skandia Jubilee Volume, Stockholm, 1955). Let the independent parameter of such a process be denoted by τ, with the origin at the point of departure of the process and on a scale independent of the number of expected changes of the random function. Denote with p(τ, n)dt the asymptotic expression for the conditional probability of one change in the random function while the parameter passes from τ to τ + dτ: relative to the hypothesis that n changes have occurred, while the parameter passes from 0 to τ. Assume further—unless the contrary is stated—that the probability of more than one change, while the parameter passes from τ to τ + dτ, is of smaller order than dτ.     

我国保险格式条款行政监管比较分析

保险合同行政监管是各种保险合同监管方式中最早的一种,同时也是必不可少的一种。我国历来重视对保险格式条款的行政监管。《合同法》、2009年修订的《保险法》、《消费者权益保护法》以及不少地方性法规都不同程度地规定了保险合同监管的主体、内容、方式、原则、宗旨等,这些规定一方面整体确立了保险监管的基本框架,同时又划分了监管主体各自的监管疆界。     

A hyperbolic diffusion model for stock prices

In the present paper we consider a model for stock prices which is a generalization of the model behind the Black–Scholes formula for pricing European call options. We model the log-price as a deterministic linear trend plus a diffusion process with drift zero and with a diffusion coefficient (volatility) which depends in a particular way on the instantaneous stock price. It is shown that the model possesses a number of properties encountered in empirical studies of stock prices. In particular the distribution of the adjusted log-price is hyperbolic rather than normal. The model is rather successfully fitted to two different stock price data sets. Finally, the question of option pricing based on our model is discussed and comparison to the Black–Scholes formula is made. The paper also introduces a simple general way of constructing a zero-drift diffusion with a given marginal distribution, by which other models that are potentially useful in mathematical finance can be developed.     

Modelling the shape of the limit order book

This article develops a parsimonious way to use the shape of the limit order book to produce an estimate of the asset price. The posited model captures and describes the evolution of the distribution of limit orders on the bid and ask sides of the LOB during the trading session and provides estimates of the execution asset price over time. The performance of the model is evaluated against some existing standards from the market microstructure literature during the trading session. Empirical evidence on listed companies confirm a strong contribution of our methodology to the innovation in asset prices, according to the information share coefficients. We also document a significant improvement relative to the Hasbrouck [J. Finance, 1991, 46, 179–207] model when our model estimates are included as regressors.     

海南省被征地农民基本养老保险项目投资收益需求测算

目前,为保障被征地农民的利益,相关省市已陆续出台了被征地农民养老保险的相关政策。为了满足养老金的支付需求,必须对资金的投资收益需求进行测算。依据海南省颁布的《海南省被征地农民基本养老保险暂行办法》(下称《暂行办法》)的相关规定,本文对海南省被征地农民养老保险资金的投资收益率需求做了测算,并对性别比例、平均年龄、消费价格指数等因素进行了敏感性分析。     

Ruin probability at a given time for a model with liabilities of the fractional Brownian motion type: A partial differential equation approach

In this paper we study the ruin probability at a given time for liabilities of diffusion type, driven by fractional Brownian motion with Hurst exponent in the range (0.5, 1). Using fractional Itô calculus we derive a partial differential equation the solution of which provides the ruin probability. An analytical solution is found for this equation and the results obtained by this approach are compared with the results obtained by Monte-Carlo simulation.     

A market model with medium/long-term effects due to an insider

In this article, we consider a modification of the Karatzas–Pikovsky model of insider trading. Specifically, we suppose that the insider agent influences the long/medium-term evolution of Black–Scholes type model through the drift of the stochastic differential equation. We say that the insider agent is using a portfolio leading to a partial equilibrium if the following three properties are satisfied: (a) the portfolio used by the insider leads to a stock price which is a semimartingale under his/her own filtration and his/her own filtration enlarged with the final price; (b) the portfolio used by the insider is optimal in the sense that it maximises the logarithmic utility for the insider when his/her filtration is fixed; and (c) the optimal logarithmic utility in (b) is finite. We give sufficient conditions for the existence of a partial equilibrium and show in some explicit models how to apply these general results.     

Pricing the Risks of Default: A Note on Madan and Unal

In their well-known article, Madan and Unal (1998) presented one of the first intensity-based credit risk models. In this approach the default intensity is directly linked to the market value of the firm's equity. In order to derive the probability of default Madan and Unal have to solve a partial differential equation (PDE). Here, we show that one of the transformations in the derivation of the solution of this PDE is not correct and analyze the difference between the correct solution of the PDE and the solution based on the incorrect transformation. As a consequence of the transformation error the credit risk of a debtor is systematically underestimated.     

The equilibrium price of futures contracts: A result drawn from capital asset pricing model

A recent study shows that separation theorems in the stock and forward market literatures may not hold in an integrated financial market; therefore, the securities market may influence futures trading. This article investigates the securities market influence on the futures price. The result shows that although the futures price incorporates the investor's expectation about the future spot price, it generally is not a best estimate of the spot price. In addition, it is shown that the speculative activity can destabilize the cash market for some commodities, if initially, the underlying cash price is highly volatile.     

我国保险保障基金风险费率模拟分析

常用的保险保障基金征收方法分为平均比率费率法和风险费率法。与国际上大多数国家一样,我国保险保障基金目前采用平均比率费率法。平均比率费率法不与保险公司自身的风险挂钩,不会因为其冒险行为而收取更高费率;而风险费率法则是保险公司风险程度与其所交的保险保障基金费率呈正比。本文对我国25家财险公司和25家寿险公司进行风险等级分类,对我国保险保障基金风险费率进行模拟分析,提出了我国保险保障基金宜采用风险费率征收方式的基本构想,体现出公平合理、防范风险的发展要求。     

A PDE method for estimation of implied volatility

In this paper it is proved that the Black–Scholes implied volatility satisfies a second order non-linear partial differential equation. The obtained PDE is then used to construct an algorithm for fast and accurate polynomial approximation for Black–Scholes implied volatility that improves on the existing numerical schemes from literature, both in speed and parallelizability. We also show that the method is applicable to other problems, such as approximation of implied Bachelier volatility.