Using the Hull and White Two Factor Model in Bank Treasury Risk Management

In order to manage interest rank risk exposure, bank treasurers allocate their portfolio of assets and liabilities to what they call standard “buckets”. In order words the portfolio of cash flows from assets and liabilities at various times are re-expressed as a portfolio of cash flows at certain specified standard times. These specified times usually correspond to important dates like expiry dates of hedging instruments (bank bills, bank bill futures, interest rate swaps, and so on). The exact choice of these dates will not concern us in this paper, but will be specified by the users of these results. Of course, this procedure can only be done in an approximate way. Traditionally, the real cash flows are assigned so that the portfolio of assets and liabilities of the bank portfolio match the portfolio of bucketed assets with respect to present value and (Macaulay) duration (or other risk measures like Reddington convexity), which could hold for a short time interval. We will not review the various methods used by practitioners, but present a method based on the use of Wiener Chaos expansions, (with respect to suitable forward probability measures), of assets and liabilities and to select bucketing in order to match various orders of the chaos expansion in the assets and liabilities portfolio and bucketed portfolio. In fact matching the first three orders of the chaos expansion is closely related to present value, duration, and convexity matching, (see Brace and Musiela [1]). In this framework it is possible to study and give results about optimal assignments, so that matching may hold over a working time horizon (a day, a week, and so on). Once assets and liabilities have been bucketed, the interest rate or exposure can be managed by the use of standard treasury products. This can involve a similar procedure to the one we have described already, by which we represent the bucketed cash flows in terms of the cash flows of a portfolio of hedging instruments.