Assumption Of Interest Rates Research Articles

Stochastic Chain-Ladder Reserving with Modeled General Inflation

We consider two possible approaches to the problem of incorporating explicit general (i.e., economic) inflation in the non-life claims reserve estimates and the corresponding reserve SCR, defined—as in Solvency II—under the one-year view. What we call the actuarial approach provides a simplified solution to the problem, obtained under the assumption of deterministic interest rates and absence of inflation risk premia. The market approach seeks to eliminate these shortcomings by combining a stochastic claims reserving model with a stochastic market model for nominal and real interest rates. The problem is studied in details referring to the stochastic chain-ladder provided by the Over-dispersed Poisson model. The application of the two approaches is illustrated by a worked example based on market data.

British Put Option On Stocks Under Regime-Switching Model

In a plain vanilla option, its holder is given the right, but not the obligation, to buy or sell the underlying stock at a specified price (strike price) at a predetermined date. If the exercise date is at maturity, the option is called a European; if the option is exercised anytime prior to maturity, it is called an American. In a British option, the holder can enjoy the early exercise feature of American option whereupon his payoff is the ‘best prediction’ of the European payoff given all the information up to exercise date under the hypothesis that the true drift of the stock equals a specified contract drift. In this paper, in contrast to the constant interest rate and constant volatility assumptions, we consider the British option by assuming that the economic state of the world is described by a finite state continuous-time Markov chain. Also, we provide a solution to a free boundary problem by using PDE arguments. However, closed form expression for the arbitrage-free price are not available in our setting.

Analysing the Impact of the Monetary Policy Dynamics on Financial Imbalances- A Model Approach

This paper employs a quarterly time series to determine the timing of structural breaks for interest rates in USA over the last 60 years. The Chow test is used for investigating the non-stationary, where the date of the potential break is assumed to be known. Moreover, an empirically examination of the financial sector to check if it is positively related to deviations from an assumed interest rate as given in a standard Taylor rule. The empirical analysis is strengthened by analysing the rule from a historical perspective and look at the effect of setting the interest rate by the central bank on financial imbalances. The empirical evidence indicates that deviation in monetary policy has a potential causal factor in the build up of financial imbalances and the subsequent crisis where macro prudential intervention could have beneficial effect. Thus, my findings tend to support the view which states that the probable existence of central banks has been one source of global financial crisis since the past decade.

Utilitarian versus neutralitarian design of endowment fund policies

ABSTRACT This paper addresses investment and spending policies of endowment funds aiming to generate a stable income stream in perpetuity. The standard academic approach to the design of such policies is based on optimization of utility aggregated over time. However, the explicit purpose of many funds to serve current and future generations ‘in equal measure’ suggests incorporation of a suitable notion of neutrality. The utilitarian and neutralitarian approaches are compared in two settings: one in which the preferences of individual generations are described by a standard CRRA utility function, and one in which these utility functions are modified by the introduction of a saturation level. Results are expressed in terms of the implied assumed interest rate (AIR), which reflects the apportionment of initially available capital to the time-0 values of individual future benefits. Under CRRA preferences, the neutralitarian point of view can be seen as a way of determining the discount factor that is used in the utilitarian method. When a saturation level is added, the neutralitarian and utilitarian policies are essentially different. The introduction of saturation generally induces a shift of value from earlier to later generations.

Profitability of Energy Supply Contracting and Energy Sharing Concepts in a Neighborhood Energy Community: Business Cases for Austria

To ensure broad application of renewable and energy-efficient energy systems in buildings and neighborhoods, profitable business models are vital. Energy supply contracting helps building residents to overcome the barrier of high upfront investment costs while additionally reducing risks related to energy-saving mechanisms. This study examines profitability for energy contractors in a variety of business cases that simultaneously ensure energy cost savings for the residents. A mixed-integer linear optimization model is developed for a neighborhood energy community, consisting of three buildings with diverse usages. In the process, the optimum capacities of building-attached and building-integrated photovoltaics, a heat pump and a gas-fired mini combined heat and power unit are determined to cover the energy community’s electricity and heat load. Results show that cross-domain contracting within energy communities is highly profitable for both, the contractor and the residents, while the extent depends on the accounting method, assumed interest rate and depreciation time. The additional application of energy-efficiency measures in/on the buildings, constituting a combination of energy supply and energy performance contracting, further increases profitability. The investigation of several sensitivities shows that high grid energy costs for electricity and gas enhance profitability of local energy technologies, leading to an increase in optimal technology capacities.

$$r-g<0$$: Can We Sleep More Soundly?

Contrary to the traditional assumption of interest rates on government debt exceeding economic growth, negative interest-growth differentials became prevalent after the global financial crisis and before the COVID-19 pandemic. Should negative differentials be grounds for sleeping more soundly, despite high government debts? We analyze interest-growth differentials using data on average effective borrowing costs for 55 countries over up to 200 years. Negative differentials prevail for both advanced and emerging economies. Even so, several default episodes have followed periods of negative differentials, and differentials are no higher prior to defaults than in normal times. Marginal (rather than average) government borrowing costs often rise sharply, but just preceding default. Based on these results, our answer is: not really.

Interest Rate in Pension Plan Premium Calculation

This research aims to analyze the relationship between the interest rate relationship is inversely proportional to the amount of the premium on the pension plan. The method used is to measure several variables, among others FSL (Future Service Liability), PVFSAL (Present Value Future Salary), PR (Pension Rate) and Premiums. Calculation, life annuity uses actuarial assumptions, one of which is the interest rate assumption, if the assumptions used are not in accordance with the actual conditions, then what happens is excessive payments or deficient payments. The interest rate has an influence in the process of calculating the defined benefit pension plan premium. Using the assumption of different interest rates (11%, 12 % and 13%), it is found that the interest rate relationship is inversely proportional to the amount of the premium. The results of this study are FSL, PVFSAL, PR and Premiums for the interest of 11%, 12% and 13% (participants aged 25 years) as follows 720,187.97; 554,000,24; 430,570.07 (FSL in Rupiah); 27,155,187.70; 24,922,770,59; 23,002,699.40 (PVFSAL in Rupiah); 2.6521; 2.2229; 1.8718 (PR in%) and 55,535.38; 46,546.85; 39,196.00 (Premiums in Rupiah)The higher the interest rate, the smaller the pension premium and vice versa.

Effects of diameter distribution errors on stand management decisions according to a simulated individual tree detection

Key MessageTree-level forest inventory data are becoming increasingly available, which motivates the use of these data for decision-making. However, airborne inventories carried out tree-by-tree typically include systematic errors, which can propagate to objective function variables used to determine optimal forest management. Effects of under-detection focused on the smallest trees on predicted immediate harvest profits and future expectation values were assessed assuming different sites and interest rates. Management decisions based on the erroneous information caused losses of 0–17% of the total immediate and future expected income of Scots pine stands.ContextOptimal decisions on how to manage forest stands can depend on the absence or presence of intermediate and understory trees. Yet, these tree strata are likely prone to inventory errors.AimsThe aim of this study is to examine implications of making stand management decisions based on data that include systematic errors resembling those typically observed in airborne inventories carried out tree-by-tree.MethodsStand management instructions were developed based on theoretical diameter distribution functions simulated to have different shape, scale, and frequency parameters corresponding to various degrees of under-detection focused on the smallest trees. Immediate harvest income and future expectation value were derived based on various management alternatives simulated.ResultsErrors in diameter distributions affected the predicted harvest profits and future expectation values differently between the simulated alternatives and depending on site type and interest rate assumptions. As a result, different alternatives were considered as optimal management compared to the use of the error-free reference distributions. In particular, the use of no management or most intensive management alternatives became preferred over alternatives with intermediate harvesting intensities. Certain harvesting types such as thinning from below became preferred more often than what was optimal. The errors did not affect the selection of the management alternative in 71% of the simulations, whereas in the remaining proportion, relying on the erroneous information would have caused losing 2%, on average, and 17% at maximum, of the total immediate and future expected income.ConclusionThe effects above might not have been discovered, if the results were validated for inventory totals instead of separately considering the immediate and future income and losses produced by the erroneous decisions. It is recommended not to separate but to integrate the inventory and planning systems for well-informed decisions.

R minus g negative

Contrary to the traditional assumption of interest rates on government debt exceeding economic growth, negative interest-growth differentials have become prevalent since the global financial crisis. As these differentials are a key determinant of public debt dynamics, can we sleep more soundly, despite high government debts? Our paper undertakes an empirical analysis of interestgrowth differentials, using the largest historical database on average effective government borrowing costs for 55 countries over up to 200 years. We document that negative differentials have occurred more often than not, in both advanced and emerging economies, and have often persisted for long historical stretches. Moreover, differentials are no higher prior to sovereign defaults than in normal times. Marginal (rather than average) government borrowing costs often rise abruptly and sharply, but just prior to default. Based on these results, our answer is: not really.

R Minus G Negative: Can We Sleep More Soundly?

Contrary to the traditional assumption of interest rates on government debt exceeding economic growth, negative interest-growth differentials have become prevalent since the global financial crisis. As these differentials are a key determinant of public debt dynamics, can we sleep more soundly, despite high government debts? Our paper undertakes an empirical analysis of interestgrowth differentials, using the largest historical database on average effective government borrowing costs for 55 countries over up to 200 years. We document that negative differentials have occurred more often than not, in both advanced and emerging economies, and have often persisted for long historical stretches. Moreover, differentials are no higher prior to sovereign defaults than in normal times. Marginal (rather than average) government borrowing costs often rise abruptly and sharply, but just prior to default. Based on these results, our answer is: not really.

THE EFFECT OF THE ASSUMED INTEREST RATE AND SMOOTHING ON VARIABLE ANNUITIES

AbstractIn this paper, we consider the risk–return trade-off for variable annuities in a Black–Scholes setting. Our analysis is based on a novel explicit allocation of initial wealth over the payments at various horizons. We investigate the relationship between the optimal consumption problem and the design of variable annuities by deriving the optimal so-called assumed interest rate for an investor with constant relative risk aversion preferences. We investigate the utility loss due to deviations from this. Finally, we show analytically how habit-formation-type smoothing of financial market shocks over the remaining lifetime leads to smaller year-to-year volatility in pension payouts, but to increases in the longer-term volatility.

Discrete-time market models from the small investor point of view and the first fundamental-type theorem

Abstract In this paper, we discuss the no-arbitrage condition in a discrete financial market model which does not hold the same interest rate assumptions. Our research was based on, essentially, one of the most important results in mathematical finance, called the Fundamental Theorem of Asset Pricing. For the standard approach a risk-free bank account process is used as numeraire. In those models it is assumed that the interest rates for borrowing and saving money are the same. In our paper we consider the model of a market (with d risky assets), which does not hold the same interest rate assumptions. We introduce two predictable processes for modelling deposits and loans. We propose a new concept of a martingale pair for the market and prove that if there exists a martingale pair for the considered market, then there is no arbitrage opportunity. We also consider special cases in which the existence of a martingale pair is necessary and the sufficient conditions for these markets to be arbitrage free.

Credit ratings and convertible bond prices: a simulation-based valuation

ABSTRACTThis study presents a simulation-based model of convertible bond prices under the assumption of stochastic interest rates. The model is developed such that the convertible bond price explicitly depends on the credit rating at the time of issuance. Key ideas explored in this study include terminating the simulated sample path immediately when the issuer defaults on the bond at time t, which is the same as the investor and the issuer optimally exercising their options and discounting the resulting cash flows at a risk-free rate. In turn, the defaulted group of sample paths belongs to the bottom xth percentile of the realized stock prices at each time, which is exogenously given by the cumulative or marginal default probability of a firm that has the same rating as the issuer. Upon calibrating the model, we can see that the moneyness of convertible bonds is strongly responsible for influencing the convertible bond price when the rating changes. Furthermore, the effects of stochastic interest rates are shown to be possibly significant when the interest rate risk’s market price is not zero.

Martingale Measures & Change of Measure Explained

An option is a financial instrument that allows the holder to buy or sell an underlying security in the future at an agreed strike or price set today. European options are often priced under the assumption of constant interest rates as seen in the Black-Scholes (1973) model. In interest rate markets however the underlying security is an interest rate, which cannot be assumed constant. Likewise bond markets have a similar requirement. To relax such an assumption option payoffs and prices can be evaluated as the expectation of a stochastic martingale process. In this paper we illustrate how to use the change of measure technique to evaluate the dynamics of a stochastic process. Firstly we discuss the preliminaries, namely Martingale measures and numeraires. Secondly we model interest rates as a Vasicek short rate process. Finally we outline how to apply a change of measure technique, where it can be seen that a change of measure to the terminal-forward measure allows us to evaluate model dynamics and simplify the calculation.

Natural interest rate: Assessing the stance of India’s monetary policy under uncertainty

The constant natural interest rate assumption implicit in Taylor type feedback rules to assess the stance of monetary policy could be misleading at times, particularly because of the time-varying nature of the natural interest rate. In the post crisis period, reflecting a complex web of supply side, demand side, regulatory and global factors, natural rates of both advanced and emerging economies have been estimated in the literature to have altered considerably. Using a theoretical framework that combines the essence of Ramsay’s growth model and the New-Keynesian macro-dynamics, and applying the Kalman filter estimation technique, this paper finds that India’s estimated natural real interest rate in Q4 of 2014–2015 lied in a range of 0.6%–3.1%, even though core estimates point to a narrower range of 1.6%–1.8%. These estimates indicate that the real interest rate gap was negative in India for a major part of the last about ten years when CPI inflation was persistently high, implying that monetary policy stance of the Reserve Bank was largely accommodative rather than anti-inflationary.

Term Premium Spillovers from the US to International Markets

This paper investigates how a rise in US long-term interest rates would have an effect on other international markets. We document that a significant portion of long-term interest rates is due to term premium, which can be interpreted as compensation for inflation risk. Based on an assumed interest rate shock of a 200-basis-point increase in the US term premium, we find that most economies experience a stronger response to an interest rate shock of the same magnitude following the taper tantrum episode in May 2013. A fixed-effect panel data regression analysis suggests that country specific fundamentals such as financial integration and inflation are crucial determinants of their response.

Zero interest rates and cross-section of stock returns

The paper presents a theoretical market system based on the tenets of Islamic finance where the underlying assumption is zero interest rate. The paper used β < 1 as a criterion for zero interest rate assumption for the theoretical market system. The paper finds using multivariate analysis on portfolios sorted on β < 1, that cross section of stock returns can be explained using a parsimnious model that incorporates both behavioural finance and fundamental finance factors.

Interest rate assumptions and predictive accuracy of central bank forecasts

The interest rate assumptions for macroeconomic forecasts differ among central banks. Common approaches are given by the assumptions that interest rates remain constant over the forecast horizon, follow a path as expected by market participants or follow a path as expected by the central bank itself. Theoretical papers such as Svensson (The instrument-rate projection under inflation targeting: the Norwegian example. Centre for European Policy Studies Working Paper (127), 2006) and Gali (J Monet Econ 58:537–550, 2011) suggest an accuracy ranking for these forecasts, from employing central bank expectations yielding the highest forecast accuracy to conditioning on constant interest rates yielding the lowest. Yet, when investigating the predictive accuracy of the Bank of England’s and the Banco Central do Brasil’s forecasts for interest rates, inflation and output growth, we hardly find any significant differences between forecasts based on the different interest rate paths. Our results suggest that the choice of the interest rate assumption appears to be of minor relevance empirically.

Banks' Stability: The effect of Monetary Policies in the light of Global Financial Crisis

&lt;p&gt;&lt;em&gt;This paper employs a quarterly time series to determine the timing of structural breaks for interest rates in USA over the last 60 years. &lt;strong&gt;The Chow test&lt;/strong&gt; is used for investigating the non-stationary, where the date of the potential break is assumed to be known. Moreover, we empirically examined the deviation from an assumed interest rate as given in a standard Taylor rule and consequences on financial sectors. The empirical analysis is strengthened by analysing the rule from a historical perspective and look at the effect of setting the interest rate by the central bank on financial imbalances. The empirical evidence indicates that deviation in monetary policy has a potential causal factor in the build up of financial imbalances and the subsequent crisis where macro prudential intervention could have beneficial effect. Thus, our findings tend to support the view, which states that the probable existence of central banks has been one source of global financial crisis since the past decade.&lt;/em&gt;&lt;/p&gt;

Exploring the total positivity of yields correlations

We test the plausibility of the total positivity assumption of interest rates changes recently introduced in order to justify the presence of shift, slope and curvature for yield curves. To this aim, we introduce and discuss a test of total positivity of order for covariance and correlation matrices. The explicit expressions of the test statistics are given for Gaussian samples and an extension to a distribution-free framework is made via a bootstrap method. After exploring with simulation the robustness of such tests, we show using real data how it is realistic to assume that correlation matrices of interest rates changes are totally positive of order two. Conclusions on total positivity of order three are more controversial.