With the recent Financial Accounting Standards Board ruling, corporations will now be responsible for publicly disclosing the market value of their derivative portfolios. This will require that each firm fairly and accurately mark-to-market their derivatives at least once every quarter. It will become increasingly important for corporates to have the tools necessary to perform the required calculations. A valuation error could have serious consequences, as shareholders will rely on the reported financial information to make investment and other decisions.
Until recently, many corporations that used derivatives have not made a meaningful investment in derivatives software. Firms often would rely on dealer mark-to-market pricing to value their derivative transactions because public disclosure was not mandatory. Alternatively, many firms would develop in-house spreadsheets that are either completely custom-made, or rely on third-party spreadsheet add-in packages, to perform their valuations. These methods provided valuations that were close estimates of the portfolio's value and were sufficient for most firms. With the recent ruling, a close estimate will not be good enough and corporations will need to review their ability to value their derivatives accurately.
The mechanics of pricing derivatives, especially interest rate derivatives, requires strict attention to detail. Even plain vanilla interest rate derivatives, such as simple caps, floors, or swaps, require forward and zero rate curves to be built for use in the valuation process. This article will show how subtle variations in building these curves can have a dramatic impact on the price of a five-year quarterly cap. This analysis assumes that the modeling of the actual derivative is correct. The magnitude of the pricing variation could increase exponentially if the derivative itself is modeled incorrectly. Consider an indexed-amortizing swap, which involves not only building a curve, but also generating reliable Monte Carlo simulations to estimate the possible rate paths for the index rate. The potential for errors in valuing such a structure is high unless pricing is done by knowledgeable people using sophisticated software.
Table 1 shows the details and pricing for a USD100 million five-year quarterly cap with a strike rate of 6.00%. The rates used to value the structure were hypothetical market rates; the rates ranged from 5.5 % for three-month LIBOR to 6 % for the five-year swap rate. A 15 % flat volatility was used to price the cap. The total premium is often referred to as a percentage of the deal's notional value. In this case, the cap is priced at 1.95%. The cap's sensitivity to a parallel shift in forward interest rates is reported as the DV01. In this case, each basis point rise in the forward rates increases the total premium by roughly two basis points. For example, if all forward rates were mis-specified by five basis points--an easily attainable error--then the price of the cap would vary by USD100,000.
First, lets examine some details of the curve-building process and how they can affect the calculated forward rates, (which are used as inputs into the cap option model). A very simple detail that is often overlooked is the basis of the underlying cap interest rate. The most common rate index used for caps is LIBOR. LIBOR is quoted on an actual/360 day count basis, which assumes that the interest rate is paid over a 360-day calendar year. But what happens if the curve is built assuming a 365-day year? Table 2 shows various rates and their actual/360 and actual/365 equivalents. For example, if the forward rate is incorrectly calculated on a 365-day year, a 7% rate would be 10 basis points higher at 7.10%. This 'minor' error in building the curve could have a meaningful impact on the derivative's value. In our example cap, the difference in value is about 13 basis points, as the cap's value using actual/365 rates is 2.08 %.
Another often-overlooked detail in curve building is the interpolation method that is chosen to calculate interest rates that lie between market points. For example, if you are trying to determine the three- and a-half-year rate, but only input the three-year and four-year swap rate, you must interpolate to calculate the answer. Table 3 shows the interpolated three- and a-half-year rate using three interpolation methods, linear, log-linear, and cubic. In this example, the interpolated rate can vary by as much as six basis points. The shape of the yield curve will determine the net valuation effect of different interpolation methods. In our example cap, because the yield curve was assumed to be reasonably flat, the interpolation method has little effect on the valuation. Using a linear or cubic interpolation will only change the price by about one basis point. However, when the yield curve is steeper than it is today, the choice of interpolation methods becomes more important.
There are many other, more complicated decisions that can influence the price of an interest rate derivative. Should one use a flat volatility or a term structure of volatility? Should an analytical model such as Black-Scholes be used, or is a numerical model better suited to value the derivative? Should cash rates, futures rates, or both be used to build the curve? When the complexity of the deal increases the variation in pricing increases and therefore correct valuation techniques become even more important.
The key to accommodating all these variables is to find a flexible system which allows the user to set the valuation parameters so that the calculated prices match market prices. The introduction of the FASB ruling requires all entities with derivatives on their books to disclose the market value of these trades. As illustrated above, this can be a very complex undertaking that requires careful analysis.
This week's Learning Curve was written bySteve Pelletier, vice president of Theoretics, a Park City, Utah-based financial software company.
