Şule Şahin

Yet More on a Stochastic Economic Model: Part 1: Updating and Refitting, 1995 to 2009

Abstract In this paper we review the Wilkie asset model for a variety of UK economic indices, including the Retail Prices Index, both without and with an ARCH model, the wages index, share dividend yields, share dividends and share prices, long term bond yields, short term bond yields and index-linked bond yields, in each case by updating the parameters to June 2009. We discuss how the model has performed from 1994 to 2009 and estimate the values of the parameters and their confidence intervals over various sub-periods to study their stability. Our analysis shows that the residuals of many of the series are much fatter-tailed than in a normal distribution. We observe also that besides the stochastic uncertainty built into the model by the random innovations there is also parameter uncertainty arising from the estimated values of the parameters.

Yet more on a stochastic economic model: part 2: initial conditions, select periods and neutralising parameters

Abstract In this paper, we consider a number of practical and theoretical aspects of the Wilkie asset model, many of which apply to any similar model used for simulation over time. We discuss the experience of the Wilkie model since 2009. We then discuss the variables that can form the working set, the input set and the output set, all of which may be different. There are different ways of simulating, either in a linear parallel structure or in a branching tree structure. We then discuss the initial conditions required, which may be market conditions at some date, or may be “neutral” initial conditions, which may be defined in different ways. One method of generating initial conditions would be to simulate them randomly, from their own long-term distribution, and we show how to calculate the means, variances and covariances of these. What we call “neutralising parameters” may have a role, and we discuss how these may be found. Finally, we suggest using additional information in the first periods of the simulation to adjust the formulae or parameters for a limited “select period”.

A Minimum Pension Guarantee Application for the Individual Pension System in Turkey: A Gendered Approach

This study examines the minimum pension guarantee (MPG), a promise by government or pension fund management that at retirement, a persons annuitized benefit will be above a prespecified minimum level. For the first time, we use an actuarial model to discuss the role of MPG in lessening the gender gaps in pension incomes in the Individual Pension System of Turkey. Our results reveal that women would be more likely than men to receive pension subsidies and would require larger pension subsidies for every combination of investment decision and years of pension participation if MPGs were implemented.

Yet more on a stochastic economic model: Part 3C: stochastic bridging for share yields and dividends and interest rates

Abstract This is the third and last subpart of a long paper in which we consider stochastic interpolation for the Wilkie asset model, considering both Brownian bridges and Ornstein–Uhlenbeck (OU) bridges. In Part 3A, we developed certain properties for both these types of stochastic bridge, and in Part 3B we investigated retail prices and wages. In this paper, we investigate the remainder of many of our data series, relating to shares and interest rates. We conclude that, regardless of the form of the annual model, the monthly data within each year can be modelled by Brownian bridges, usually on the logarithm of the principal variable. But in no case is a simple Brownian bridge enough, and all series have their own peculiarities. Overall, however, our modelling produces simulations that are realistic in comparison with the known data. Many of our findings would apply to any similar model used for simulation over time. Our results have considerable importance for financial economics. We reconcile the conflict between the long-term mean-reverting modelling of Schiller and the short-term random walk modelling of Fama. This conclusion therefore has very wide significance.

Yet more on a stochastic economic model: Part 3B: stochastic bridging for retail prices and wages

Abstract This is the second subpart of three in a long paper in which we consider stochastic interpolation for the Wilkie asset model, considering both Brownian bridges and Ornstein–Uhlenbeck (OU) bridges. In Part 3A, we developed certain properties for both these types of stochastic bridge, and we investigate the properties of many of our data series on the same lines. We have several economic or investment series, which all have their own peculiarities. In this paper, we cover only retail prices and wages. The other series are dealt with in Part 3C. We find that, although the annual series for the rate of inflation is generated by an AR(1) model, which is the discrete time equivalent of an OU process, an OU bridge is not suitable. We need to use a Brownian bridge on the logarithm of the Price Index. Further, the standard deviation of the monthly increments in any year is, as we find empirically from the data, a function of the change in the annual value, and further there is correlation between the monthly increments in successive years.

Pricing pension buy-outs under stochastic interest and mortality rates

Abstract Pension buy-out is a special financial asset issued to offload the pension liabilities holistically in exchange for an upfront premium. In this paper, we concentrate on the pricing of pension buy-outs under dependence between interest and mortality rates risks with an explicit correlation structure in a continuous time framework. Change of measure technique is invoked to simplify the valuation. We also present how to obtain the buy-out price for a hypothetical benefit pension scheme using stochastic models to govern the dynamics of interest and mortality rates. Besides employing a non-mean reverting specification of the Ornstein–Uhlenbeck process and a continuous version of Lee–Carter setting for modeling mortality rates, we prefer Vasicek and Cox–Ingersoll–Ross models for short rates. We provide numerical results under various scenarios along with the confidence intervals using Monte Carlo simulations.

Optimal lower barrier on modified surplus process

ABSTRACT We obtain the optimal pair of initial surplus and barrier level under the lower barrier model on the modified surplus process. In particular, we examine the defective distribution function of the time to ruin with lower barrier k and initial surplus u which is suggested by Nie et al. [Minimizing the ruin probability through capital injections. Ann Actuar Sci. 2011;5(2):195–209]. We aim to take this approach one step further by proposing optimal reinsurance under the minimum finite time ruin probability and maximum benefit criteria such as the released capital, expected profit and expected utility. We calculate the optimal pairs of initial surplus and barrier levels for different time periods, loading factors and weights of the criteria. In decision-making process, we use the Technique for Order of Preference by Similarity to Ideal Solution method with Mahalanobis distance. We analyse the robustness of the results with sensitivity analysis.

A yield-macro model for actuarial use in the United Kingdom

Abstract We construct yield curve models for the UK nominal, real and implied inflation spot rates considering the linkage between their term structures and some macroeconomic variables, in particular, realised inflation and real GDP growth. The paper extends the benchmark “yield-only” model proposed by Şahin et al. (2014) by exploring the bidirectional relations between the yield curve factors and the macroeconomic variables and proposes a “yield-macro” model. Although a simple autoregressive order one process fits the yield curve factors quite well the insertion of some macroeconomic variables such as realised inflation and real GDP growth improves the models significantly. We also model macroeconomic variables that take the term structures into account and compare the yield-macro model with Wilkie’s model both philosophically and empirically.

A yield-only model for the term structure of interest rates

Abstract This paper develops a term structure model for the UK nominal, real and implied inflation spot zero-coupon rates simultaneously. We start with fitting a descriptive yield curve model proposed by Cairns (1998) to fill the missing values for certain given days at certain maturities in the yield curve data provided by the Bank of England. We compare four different fixed ‘exponential rate’ parameter sets and decide the set of parameters which fits the data best. With the chosen set of parameters we fit the Cairns model to the daily values of the term structures. By applying principal component analysis on the hybrid data (Bank of England data and fitted spot rates for the missing values) we find three principal components, which can be described as ‘level’, ‘slope’ and ‘curvature’, for each of these series. We explore the relation between these principal components to construct a ‘yield-only’ model for actuarial applications. Main contribution of this paper is that the models developed in the paper enable the practitioners to forecast three term structures simultaneously and it also provides the forecast for whole term structures rather than just short and long end of the yield curves.