# Gap Reports: Reporting on Options Related Positions

Many consumer products have embedded options in them because the customer has the right to change the terms of a contract or to act when warranted by market conditions. When a customer exercises the option, the bank loses a valuable asset that will no longer pay interest. Since these products are germane to a bank’s interest rate risk exposure, institutions should incorporate them into their gap reports.

In a product with an embedded option, the cash flows will depend on the path of interest rates; different interest rate paths need to be considered because of the dates of the options exercise will change accordingly, affecting cash flows. A single gap report gives an incomplete picture of products with embedded options because it allows for only repricing date.

Three methods of incorporating options exposures into gap reports are popular with banks. An examiner encountering a bank using another method should analyse the approach to determine whether it properly incorporates the asymmetrical impact of options on future net interest income and economic value.

The first method either recognizes that the cap is in full effect for the remaining life of the product or ignores it for the same period. The following example illustrates this all or nothing approach to a cap on a floating rate loan:

The bank has a 10-year $100,000 floating rate loan that reprices every six months but is subject to a 12 percent lifetime cap (the rate of the loan cannot exceed 12%). The all-or-nothing approach would consider the loan a six-month floating rate loan when rates are below 12%. If rates equal or exceed 12%, the loan becomes a fixed rate loan wit a 10-year repricing maturity. This approach has several weaknesses. First, the method does not correctly reflect the exposure of net interest income to future changes in interest rates. For example, when the loan is slotted as a six-month repricing asset and funded with a six month CD, the gap report would not indicate any interest rate risk. If interest rates were to rise above 12%, however, the loan could not reprice further but the funding costs on the CD could continue to rise, and interest margins would decline. Second, this treatment does not suggest how this exposure may be hedged. Neither hedging the asset as a six-month floating rate asset nr hedging it as a 10 year fixed rate asset would be appropriate. A better approach would be for the bank to prepare two gap reports, one for a high rate scenario and the other for a low-rate scenario. Under the high rate scenario the cap would be binding and the gap report would show the capped loans as fixed rate assets. Under the low rate scenario, the gap report would show the loan as a floating rate asset. A bank could use similar approaches to measure prepayment option risks associated with a fixed residential mortgage loans. Under the high-rate scenario, the weighted average lives of the fixed rate mortgages would be extended in the gap report, reflecting the effect of slower repayments. Under the low-rate scenario, the weighted lives would be shortened, reflecting faster prepayments. Comparing the gaps, between the two schedules provides an indication of the amount of option risk the bank faces. Although this second method provides a way to assess how embedded options may alter a bank’s repricing imbalances under alternative interest rate scenarios, it also has limitations. Like all-or-nothing approach this method suggests that an option has value only when it becomes binding or is in the money. In reality, an option has value throughout its life. The value of the option will depend on such factors as the time to expiration of the option, the distance from the strike price, and the volatility of interest rates. A third approach for incorporating options into gap reports varies the value of the option according to the change in the value of the underlying instrument. This is done by incorporating the delta-equivalent value of the option into the gap report. The delta-equivalent value of an option, a mathematically derived weighting between 0 % and 100%, reflects the probability that the option will go in the money. In the illustration of the loan with the 12 percent lifetime cap described above, the bank would strip the cap from the loan and treat the cap as a six-month floating rate loan and the cap as an off-balance sheet instrument, based on the cap’s delta equivalent value. The delta-equivalent value. The delta-equivalent value would equal the delta of the cap times the notional value of the cap (in this case, the principal amount of the loan, or$100,000).

The cap in this example would have a delta between 50% and 100% when rates are higher than 12%. The high level of the delta indicates a high probability of the cap being effective over the life of the loan. If market rates were 8%, however, the delta would be much lower, reflecting a lower probability that the cap will be effective over the life of the loan.

The delta approach also has limitations. The delta of an option in a nonlinear fashion with the passage of time and with the level of interest rates. As a result the delta value of an option is valid only for small changes in interest rates, and this value changes over time.

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