Liability Cash Flows Research Articles

Liquidity risk and market value of insurance companies in Nigeria

The study examines the market value effect of liquidity risk of insurance companies in Nigeria. Liquidity risk has caused market value related problems and even insolvencies in the Nigeria insurance industry in the past and it remains a key risk for insurance companies to manage it now and in the future. Twenty seven (27) quoted insurance companies were used in the study. Ex-post facto research design method was also employed while the panel data were sourced from the Securities and Exchange Commission (SEC) Statistical Bulletin, Nigerian Stock Exchange (NSE) and Audited Annual Financial Reports of the studied companies from 2004 to 2023. This research adopts stationarity test, cointegration test, and pooled least squares regression test methods. The finding shows that there are significant influences of liquidity ratio, leverage ratio and firm size on market value of insurance companies in Nigeria (p = 0.0000, 0.0019 & 0.0000 < 0.05). This study concludes that there is a significant market value effect of liquidity risk of insurance companies in Nigeria. Insurance companies should have enough cash to meet their obligations both in short run and long run. There is need for regular cash flow modeling, which can project potential liquidity needs from the liability side of the balance sheet. Also, a liquidity-adjusted assets analysis can be applied to asset positions to estimate the cost of supplying liquidity from the asset side of the balance sheet to match those liability cash flow needs.

Multiple-prior valuation of cash flows subject to capital requirements

We study market-consistent valuation of liability cash flows motivated by current regulatory frameworks for the insurance industry. The value assigned to an insurance liability is the consequence of (1) considering a hypothetical transfer of an insurance company's liabilities, and financial assets intended to hedge these liabilities, to an empty corporate entity, and (2) considering the circumstances under which a capital provider would want to achieve and maintain ownership of this corporate entity given limited liability for the owner and that capital requirements have to be met at any time for continued ownership.We focus on the consequences of the capital provider assessing the value of continued ownership in terms of a least favorable expectation of future dividends, meaning that we consider expectations with respect to probability measures in a set of equivalent martingale measures. We show that natural conditions on the set of probability measures imply that the value of a liability cash flow is given in terms of a solution to a backward recursion. Through a life and a non-life insurance example we demonstrate how to make the valuation approach operational.

Financial Fasilitation to Support Commercialization of Superior Breed Innovation

Livestock products innovation, especially of those superior breed have become one of the solution in the development of livestock production, where in reality is very limited on the availability of good quality breed. Indonesian Agency of Agricultural Research and Development through Indonesian Center for Animal Research and Development Implementing Units have been responsed these needs through breeding research started in the year of 2000. This effort have been yielded some superior local breeds, i.e. beef cattle, sheep, goats, chicken, duck and rabbit that are ready to disseminate to the community, especially for farmers. The dissemination of these superior breeds may enabling to expand and reach its distribution massively to increase animal production. One of the determinant factor to develop the process of its development is availability of financial access, which most farmers in general are very much constrained by capital asset. Therefore, facilitation support is needed to increase capital capacity that is impartial and accommodates the business characteristics. Objective of the manuscript is to review of facilitation support needed of the superior breed innovative research that disseminate to maintain sustainability of its development. In recent years, the Government has launched program of People’s Busines Credit (KUR) that could be optimized to scalling up farmers’ farming with good quality breed. Bank accessibility has demanded to have economics size of scale to be financed in order to guarantee profitable business with its liability cash flow. Meanwhile, livestock farming had been dominated by small scale farmers and yet for production oriented to reach its profitability. Supervision and technical guidance need to be consistently assisted to farmers as prospectous KUR debitor program in order to accelerate the process on disbursement of credit to supply their capital asset.

Extended reduced-form framework for non-life insurance

AbstractIn this paper we propose a general framework for modeling an insurance liability cash flow in continuous time, by generalizing the reduced-form framework for credit risk and life insurance. In particular, we assume a nontrivial dependence structure between the reference filtration and the insurance internal filtration. We apply these results for pricing and hedging non-life insurance liabilities in hybrid financial and insurance markets, while taking into account the role of inflation under the benchmarked risk-minimization approach. This framework offers at the same time a general and flexible structure, and an explicit and treatable pricing-hedging formula.

A Large-Scale Optimization Model for Replicating Portfolios in the Life Insurance Industry

Replicating Portfolios for Economic Capital Calculations

Stochastic modeling of assets and liabilities with mortality risk

ABSTRACT This paper describes a general approach for the stochastic modeling of assets returns and liability cash-flows of a typical pensions insurer. On the asset side, we model the investment returns on equities and various classes of fixed-income instruments including short- and long-maturity fixed-rate bonds as well as index-linked and corporate bonds. On the liability side, the risks are driven by future mortality developments as well as price and wage inflation. All the risk factors are modeled as a multivariate stochastic process that captures the dynamics and the dependencies across different risk factors. The model is easy to interpret and to calibrate to both historical data and to forecasts or expert views concerning the future. This feature is particularly useful in unprecedented circumstances like pandemics when historical data alone does not give a reasonable description of the future. The simple structure of the model allows for efficient computations. The construction of a million scenarios takes only a few minutes on a personal computer. The approach is illustrated with an asset-liability analysis of a defined benefit pension fund, pre- and post-COVID-19.

Continuous-time limits of multi-period cost-of-capital margins

Abstract We consider multi-period cost-of-capital valuation of a liability cash flow subject to repeated capital requirements that are partly financed by capital injections from capital providers with limited liability. Limited liability means that, in any given period, the capital provider is not liable for further payment in the event that the capital provided at the beginning of the period turns out to be insufficient to cover both the current-period payments and the updated value of the remaining cash flow. The liability cash flow is modeled as a continuous-time stochastic process on [ 0 , T ] {[0,T]} . The multi-period structure is given by a partition of [ 0 , T ] {[0,T]} into subintervals, and on the corresponding finite set of times, a discrete-time cost-of-capital-margin process is defined. Our main objective is the analysis of existence and properties of continuous-time limits of discrete-time cost-of-capital-margin processes corresponding to a sequence of partitions whose meshes tend to zero. Moreover, we provide explicit expressions for the limit processes when cash flows are given by Itô diffusions and processes with independent increments.

Time Consistent Solvency Capital Requirement Under Solvency II.

In this paper, we analyse the current dynamic definitions of the Solvency Capital Requirement (SCR) and we propose a new dynamic and time consistent formulation of the SCR, that is compliant with the Solvency II directive. In case of a single liability cash-flow at maturity, Devolder and Lebegue (2017) analyse the time-consistent dynamic formulation of the SCR using iterated risk measures. Firstly, we extend the iterated-SCR (ISCR) formulation to the case of multiple liability cash-flows. However, the iterated formulation of the SCR presents some drawbacks. Devolder and Lebegue (2017) show that using iterated risk measures, the ISCR becomes quite expensive for long term liabilities. Moreover, we show that in case of multiple liability cash-flows, the ISCR is not completely compliant with the Solvency II directive. In fact, ISCR does not answer to a fundamental regulator request: the capital to be held by insurance company to meet obligations over the following year. Then, starting from the static definition in Christiansen and Niemeyer (2014), we propose a dynamic version of the SCR, that is time consistent and encompasses the drawbacks of the iterated formulation. Our proposed dynamic definition of the SCR, called additive-SCR (ASCR), indicates the expected total capital requirement for the period from time zero to the liabilities maturity. Moreover, the ASCR can be decomposed in the annual expected-SCRs (ESCR), which represent the expected regulatory capital for the next year, not only at time zero but also at the futures payment dates. Hence, we build a term structure of expected annual SCRs.

The value of a liability cash flow in discrete time subject to capital requirements

The aim of this paper is to define the market-consistent multi-period value of an insurance liability cash flow in discrete time subject to repeated capital requirements, and explore its properties. In line with current regulatory frameworks, the presented approach is based on a hypothetical transfer of the original liability and a replicating portfolio to an empty corporate entity, whose owner must comply with repeated one-period capital requirements but has the option to terminate the ownership at any time. The value of the liability is defined as the no-arbitrage price of the cash flow to the policyholders, optimally stopped from the owner’s perspective, taking capital requirements into account. The value is computed as the solution to a sequence of coupled optimal stopping problems or, equivalently, as the solution to a backward recursion.

Fair Valuation of Insurance Liability Cash-Flow Streams in Continuous Time: Applications

Delong et al. (2018) presented a theory of fair (market-consistent and actuarial) valuation of insurance liability cash-flow streams in continuous time. In this paper, we investigate in detail two practical applications of our theory of fair valuation. In the first example, we consider the fair valuation of a terminal benefit which is contingent on correlated tradeable and non-tradeable financial risks. In the second example, we consider a portfolio of unit-linked contracts contingent on a non-tradeable insurance and a tradeable financial risk. We derive partial differential equations (PDEs) which characterize the continuous-time fair valuation operators in these two examples. We find explicit solutions to the PDEs. The fair values of the liabilities are decomposed into the best estimate of the liability and the risk margin. The arbitrage-free representations of the fair values of the liabilities are also derived. The dynamic hedging strategies associated with the continuous-time fair valuation operators are established. Detailed interpretations of the results, which should be useful both for researchers and practitioners, are provided.

Fair Valuation of Insurance Liability Cash-Flow Streams in Continuous Time: Theory

We investigate fair (market-consistent and actuarial) valuation of insurance liability cash-flow streams in continuous time. We first consider one-period hedge-based valuations, where in the first step, an optimal dynamic hedge for the liability is set up, based on the assets traded in the market and a quadratic hedging objective, while in the second step, the remaining part of the claim is valuated via an actuarial valuation. Then, we extend this approach to a multi-period setting by backward iterations for a given discrete-time step $h$, and consider the continuous-time limit for $h\to 0$. We formally derive a partial differential equation for the valuation operator which satisfies the continuous-time limit of the multi-period, discrete-time iterations and prove that this valuation operator is actuarial and market-consistent. We show that our continuous-time fair valuation operator has a natural decomposition into the best estimate of the liability and a risk margin. The dynamic hedging strategy associated with the continuous-time fair valuation operator is also established. Finally, the valuation operator and the hedging strategy allow us to study the dynamics of the net asset value of the insurer.

Replicating portfolio approach to capital calculation

The replicating portfolio (RP) approach to the calculation of capital for life insurance portfolios is an industry standard. The RP is obtained from projecting the terminal loss of discounted asset–liability cash flows on a set of factors generated by a family of financial instruments that can be efficiently simulated. We provide the mathematical foundations and a novel dynamic and path-dependent RP approach for real-world and risk-neutral sampling. We show that our RP approach yields asymptotically consistent capital estimators if the chaotic representation property holds. We illustrate the tractability of the RP approach by three numerical examples.

Valuation of Non-Life Liabilities from Claims Triangles

This paper provides a complete program for the valuation of aggregate non-life insurance liability cash flows based on claims triangle data. The valuation is fully consistent with the principle of valuation by considering the costs associated with a transfer of the liability to a so-called reference undertaking subject to capital requirements throughout the runoff of the liability cash flow. The valuation program includes complete details on parameter estimation, bias correction and conservative estimation of the value of the liability under partial information. The latter is based on a new approach to the estimation of mean squared error of claims reserve prediction.

Insurance valuation: A computable multi-period cost-of-capital approach

We present an approach to market-consistent multi-period valuation of insurance liability cash flows based on a two-stage valuation procedure. First, a portfolio of traded financial instrument aimed at replicating the liability cash flow is fixed. Then the residual cash flow is managed by repeated one-period replication using only cash funds. The latter part takes capital requirements and costs into account, as well as limited liability and risk averseness of capital providers. The cost-of-capital margin is the value of the residual cash flow. We set up a general framework for the cost-of-capital margin and relate it to dynamic risk measurement. Moreover, we present explicit formulas and properties of the cost-of-capital margin under further assumptions on the model for the liability cash flow and on the conditional risk measures and utility functions. Finally, we highlight computational aspects of the cost-of-capital margin, and related quantities, in terms of an example from life insurance.

A Large-Scale Optimization Model for Replicating Portfolios in the Life Insurance Industry

Replicating portfolios have recently emerged as an important tool in the life insurance industry, used for the valuation of companies' liabilities. This paper presents a replicating portfolio (RP) model for approximating life insurance liabilities as closely as possible. We minimize the L1 error between the discounted life insurance liability cash flows and the discounted RP cash flows over a multi-period time horizon for a broad range of different future economic scenarios. We apply two different linear reformulations of the L1 problem to solve large-scale RP optimization problems and also present several out-of-sample tests for assessing the quality of RPs. A numerical application of our RP model to empirical data sets demonstrates that the model delivers RPs that match the liabilities rather closely. The numerical analysis demonstrates that our model delivers RPs with excellent practical properties in a reasonable amount of time. We complete the paper with a description of an implementation of the RP model at a global insurance company.

Cash flow generalisations of non-life insurance expert systems estimating outstanding liabilities

For as long as anyone remembers non-life insurance companies have used the so called chain ladder method to reserve for outstanding liabilities. When historical payments of claims are used as observations then chain ladder can be understood as estimating a multiplicative model. In most non-life insurance companies a mixture of paid data and expert knowledge, incurred data, is used as observations instead of just payments. This paper considers recent statistical cash flow models for asset–liability hedging, capital allocation and other management decision tools, and develops two new such methods incorporating available incurred data expert knowledge into the outstanding liability cash flow model. These two new methods unbundle the incurred data to aggregates of estimates of the future cash flow. By a re-distribution to the right algorithm, the estimated future cash flow is incorporated in the overall estimation process and considered as data. A statistical validation technique is developed for these two new methods and they are compared to the other recent cash flow methods. The two methods show to have a very good performance on the real-life data set considered.

Valuation of Index-Linked Cash Flows in a Heath–Jarrow–Morton Framework

In this paper, we study the valuation of stochastic cash flows that exhibit dependence on interest rates. We focus on insurance liability cash flows linked to an index, such as a consumer price index or wage index, where changes in the index value can be partially understood in terms of changes in the term structure of interest rates. Insurance liability cash flows that are not explicitly linked to an index may still be valued in our framework by interpreting index returns as so-called claims inflation, i.e., an increase in claims cost per sold insurance contract. We focus primarily on the case when a deep and liquid market for index-linked contracts is absent or when the market price data are unreliable. Firstly, we present an approach for assigning a monetary value to a stochastic cash flow that does not require full knowledge of the joint dynamics of the cash flow and the term structure of interest rates. Secondly, we investigate in detail model selection, estimation and validation in a Heath–Jarrow–Morton framework. Finally, we analyze the effects of model uncertainty on the valuation of the cash flows and how forecasts of cash flows and interest rates translate into model parameters and affect the valuation.

Manipuliacinės kūrybinės apskaitos anatomija ir jos informacijos naudojimas

In conditions of the global and competitive market, creative accounting when from accounting methods permitted in legislation not those that reveal the real situation of a company but those that show better or worse performance results for certain user groups are being selected.It is wrong to use the term of creative accounting in the context of data manipulation in order to show a better or a worse performance of a company, even with respect to applicable legislation. With the consideration of the capacity of the term ‘creative accounting’, it is important to distinguish two types of creative accounting: positive and manipulative. The aim of the positive creative accounting is to show an equitable and correct view on a company’s financial condition and performance and facilitate the work of accountants to provide a reliable and unvaried information to all of the its users. The aim of manipulative creative accounting is to provide a distorted information about the company's financial condition and performance for certain user groups by using a variety of justifying measures.There are different fields of the application of creative accounting. Of them, most widespread are tangible fixed assets, intangible assets, current assets, equity capital, liability cash flow, income, expense, profit, and tax accounting. It is difficult to reveal inconsistencies with reality for data generated by accounting, because they are carefully concealed. The benefit from using the manipulative creative accounting is usually only temporary, therefore it is important to evaluate in advance the impact of the application of manipulative creative accounting on the future performance which may worsen and also have a negative impact on the company's image.

Risk-Adjusted Pricing of Bank's Assets Based on Cash Flow Matching Matrix

To price bank’s assets correctly, it is important to know cost of funds. But funding cost calculation is complicated due to the fact that banks fund long term assets through short-term liabilities. As a result, assets with a given time to maturity are usually financed by several liabilities with different maturities. To calculate funding cost it needs to know how cash flows are matched between assets and liabilities. For this it`s used cash flow matching matrix or funding matrix. In the paper, a new algorithm of filling of a two-dimensional funding matrix that is based on the golden rule of banking and modified RAROC approach is proposed. It provides positive definiteness and uniqueness of the matrix. The matrix shows terms to maturity and amounts of liability cash flows which fund the asset cash flow with a given term to maturity. Examples of partially and fully filled matrices are presented. It is proposed an approach to risk-adjusted pricing that is based on this funding matrix and RAROC-approach adapted to cash flows. The developed approach to pricing integrates organically credit and liquidity risks. It takes into consideration expected credit losses and economic capital (unexpected credit losses) for all lifetime of asset cash flows and not one-year period traditionally used in RAROC.

Stochastic economic models for actuarial use: an example from China

AbstractIn this paper, the first study of stochastic economic modelling with Chinese data is conducted for actuarial use. Univariate models, vector autoregression and two cascade systems (equity-driving cascade system and price-inflation-driving cascade system) are described and compared. We focus on six major economic assumptions for modelling purposes, which are price inflation rate, wage inflation rate, long-term interest rate, short-term interest rate, equity total return and bond total return. Granger causality tests are used to identify the driving force of a cascade system. Robust standard errors are estimated for each model. Diagnostic checking of residuals, goodness-of-fit measures and out-of-sample validations are applied for model selection. By comparing different models for each variable, we find that the equity-driving cascade system is the best structure for actuarial use in China. The forecasts of the variables could be applied as economic inputs to stochastic projection models of insurance portfolios or pension funds for short-term asset and liability cash flow forecasting.