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Added by
Michael Coopersmith
Publication date
2011
fields
Financial
and research's language is
English
Authors
Michael Coopersmith
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A relation between interest rates and inflation is presented using a two component economic model and a simple general principle. Preliminary results indicate a remarkable similarity to classical economic theories, in particular that of Wicksell.
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We propose a class of discrete-time stochastic models for the pricing of inflation-linked assets. The paper begins with an axiomatic scheme for asset pricing and interest rate theory in a discrete-time setting. The first axiom introduces a risk-free asset, and the second axiom determines the intertemporal pricing relations that hold for dividend-paying assets. The nominal and real pricing kernels, in terms of which the price index can be expressed, are then modelled by introducing a Sidrauski-type utility function depending on (a) the aggregate rate of consumption, and (b) the aggregate rate of real liquidity benefit conferred by the money supply. Consumption and money supply policies are chosen such that the expected joint utility obtained over a specified time horizon is maximised subject to a budget constraint that takes into account the value of the liquidity benefit associated with the money supply. For any choice of the bivariate utility function, the resulting model determines a relation between the rate of consumption, the price level, and the money supply. The model also produces explicit expressions for the real and nominal pricing kernels, and hence establishes a basis for the valuation of inflation-linked securities.
We propose a new model for the joint evolution of the European inflation rate, the European Central Bank official interest rate and the short-term interest rate, in a stochastic, continuous time setting. We derive the valuation equation for a contingent claim and show that it has a unique solution. The contingent claim payoff may depend on all three economic factors of the model and the discount factor is allowed to include inflation. Taking as a benchmark the model of Ho, H.W., Huang, H.H. and Yildirim, Y., Affine model of inflation-indexed derivatives and inflation risk premium, (European Journal of Operational Researc, 2014), we show that our model performs better on market data from 2008 to 2015. Our model is not an affine model. Although in some special cases the solution of the valuation equation might admit a closed form, in general it has to be solved numerically. This can be done efficiently by the algorithm that we provide. Our model uses many fewer parameters than the benchmark model, which partly compensates the higher complexity of the numerical procedure and also suggests that our model describes the behaviour of the economic factors more closely.
A term structure model in which the short rate is zero is developed as a candidate for a theory of cryptocurrency interest rates. The price processes of crypto discount bonds are worked out, along with expressions for the instantaneous forward rates and the prices of interest-rate derivatives. The model admits functional degrees of freedom that can be calibrated to the initial yield curve and other market data. Our analysis suggests that strict local martingales can be used for modelling the pricing kernels associated with virtual currencies based on distributed ledger technologies.
We generalize a money demand micro-founded model to explain Romanians recent loss of interest for the euro. We show that the reason behind this loss of interest is a severe decline in the relative degree of the euro liquidity against that of the Romanian leu.
Modeling taxation of Variable Annuities has been frequently neglected but accounting for it can significantly improve the explanation of the withdrawal dynamics and lead to a better modeling of the financial cost of these insurance products. The importance of including a model for taxation has first been observed by Moenig and Bauer (2016) while considering a GMWB Variable Annuity. In particular, they consider the simple Black-Scholes dynamics to describe the underlying security. Nevertheless, GMWB are long term products and thus accounting for stochastic interest rate has relevant effects on both the financial evaluation and the policy holder behavior, as observed by Gouden`ege et al. (2018). In this paper we investigate the outcomes of these two elements together on GMWB evaluation. To this aim, we develop a numerical framework which allows one to efficiently compute the fair value of a policy. Numerical results show that accounting for both taxation and stochastic interest rate has a determinant impact on the withdrawal strategy and on the cost of GMWB contracts. In addition, it can explain why these products are so popular with people looking for a protected form of investment for retirement.
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