We consider the problem of identifying endogenous current coupons for To-BeAnnounced (TBA) agency mortgage pass through securities. Current coupons play a crucial role in the mortgage backed securities. The current coupon is said to be endogenous if it gives rise to a fairly, or par valued, TBA. Since prepayments both affect the value of the mortgage and depend heavily upon the coupon, the iden...

We extend the classical coupon collector’s problem to one in which two collectors are simultaneously and independently seeking collections of d coupons. We find, in finite terms, the probability that the two collectors finish at the same trial, and we find, using the methods of Gessel-Viennot, the probability that the game has the following “ballotlike” character: the two collectors are tied wi...

This paper discusses the use of parametric models for the term structure of interest rates and their uses. The paper focuses initially on a potential problem which arises out of the use of certain models. In most cases the process of parameter estimation involves the minimization or maximization of a function (for example, least squares or maximum likelihood). In some cases this function can ha...

In the field of probabilistic analysis, bounding the tail distribution is a major tool for estimating the failure probability of systems. In this paper, we present the verification of Markov’s and Chebyshev’s inequalities for discrete random variables using the HOL theorem prover. The formally verified Markov and Chebyshev’s inequalities allow us to precisely reason about tail distribution boun...

We consider a power utility maximization problem with additive habits in a framework of discrete-time markets and random endowments. For certain classes of incomplete markets, we establish estimates for the optimal consumption stream in terms of the aggregate state price density, investigate the asymptotic behavior of the propensity to consume (ratio of the consumption to the wealth), as the in...

The aim of the paper is to develop pricing formulas for European type Asian options written on the exchange rate in a two currency economy. The exchange rate as well as the foreign and domestic zero coupon bond prices are assumed to follow geometric Brownian motions. As a special case of a discrete Asian option we analyse the delayed payment currency option and develop closed form pricing and h...

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