Parallel Implementation of a Pricing Kernel for Interest Rate Dependent Products
by
Hans Moritsch
Department of Business, University of Vienna
Coauthors: E. J. Dockner (Department of Business, University of Vienna)

The pricing of interest rate dependent financial instruments is one of the most important areas in asset pricing theory. In case of simple instruments with deterministic (nondefaultable) cash flows pricing is based on an arbitrage argument on the basis of pure discount bond prices. Hence, if we have given a term structure of spot rates it is easy to derive the price of a fixed coupon bond. The theoretical price then simply is the present value of future cash flows. Many interest rate dependent products are not based on a fixed interest rate. In case of floating rate securities we have to distinguish two different classes of instruments depending on whether the maturity of the reference interest rate is smaller or equal to the period until the next interest rate adjustment takes place. In case the maturity of the reference interest rate is smaller than the adjustment period it can be shown that the price of the floater at the time of the next adjustment is equal to its face value so that the pricing of the floater is identical to that of a fixed income (deterministic cash flow) instrument. In case the maturity of the reference interest rate exceeds the period of adjustment we are faced with a so called constant maturity instrument and the pricing becomes much more involved. In particular one needs an interest rate model that allows for projections of future interest rates that can be used to forecast uncertain interest payments. Hull and White developed a single factor model that we will make use of in this paper to price constant maturity instruments.

The use of constant maturity instruments is very popular among Austrian banks. In particular instruments based on the so called secondary market yield (SMY) are frequently used. Examples include loans, credits as well as bonds that use the SMY as a reference interest rate. The SMY is an index of Austrian government bond yields currently traded in the secondary market and can be interpreted as an average yield to maturity. Since the maturity spectrum of Austrian government bonds ranges from less than one year to thirty years the time bucket to which the SMY corresponds is in the range of five to seven years. Hence, all instruments that make use of the SMY fit into the class of constant maturity floaters.

The popularity of the SMY stems from its properties given a normal shaped yield curve. If bank deposits (liabilities) have on average a short maturity and loans with the SMY as interest rate (assets) have a longer time to maturity the normal shape of the yield curve guarantees a remarkable profit for the bank. Things are, however, quite different during a period of an inverse yield curve.

Despite these arguments the pricing of constant maturity instruments is an interesting theoretical issue and becomes even more involved if the interest rate product is characterized by option features.

In this paper we take up the issue of pricing CMI's with embedded options on the basis of numerical techniques. As far as the embedded options are concerned we look at the following products. As mentioned above the use of SMY floating instruments are very popular in Austria. Moreover some of these products have the follwing type of interest rate rate adjustment. There is an initial reference rate for that applies as long as the variable interest rate does not hit a lower or an upper bound. If the variable rate (the SMY) passes the bounds an interest rate adjustment is made that depends on a factor of adjustment as well as the previous adjustment levels. Hence these products are characterized by caps and floors but the cap/floor rate depends on past interest rate realizations. Therefore the products are path dependent. To capture these characteristics we make use of the Hull and White interest rate tree model and use Monte Carlo techniques to price the instruments. Using the Hull and White trinomial tree implies that we generate an entire term structure on the basis of a single factor (risk factor) which is the short term interest rate. The flexibility of the Hull and White model, however, guarantees that the term structures generated by the tree are consistent with todays observed one. Moreover the model can be calibrated to fit the current volatility structure as well.

Making use of Monte Carlo simulation techniques together with the Hull and White interest rate tree gives us enough flexibility to price a very large spectrum of interest rate products. There is one disadvantage to this approach, however. A Monte Carlo simulation is computationally very intensive. Therefore we present two possible implementations of our model. One is a sequential version and the other one makes use of data parallel structures. We present performance evaluations based on this two implementations and sensitivity analysis as the accuracy of the pricing tool is concerned. The pricing module presented in this paper is part of a larger model that has been developed within the AURORA research program. This model fits into the category of a financial planning tool that uses stochastic optimization techniques to derive optimal financial allocation decisions.

Date received: March 1, 1999

Copyright © 1999 by the author(s). The author(s) of this document and the organizers of the conference have granted their consent to include this abstract in Atlas Conferences Inc. Document # cacq-22.