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A range structure accrues value when a reference index fixes inside a specific range during a pre-defined period.
Range Accruals
A range structure accrues value when a reference index fixes inside a specific range during a pre-defined period. It can be used for liability management purposes--as a swap leg versus a money market vanilla interest leg--or for an investment--as a coupon on an exotic EMTN, for example.
The range, determined by two barriers, can remain constant or can have evolving barriers. The expected amount of interest is therefore equal to the maximum coupon times the probability the reference index will stay within the range during the observation period.
A callable (or cancellable) instrument gives the exotic interest rate payer the option to terminate the transaction early on predetermined payment dates. The sale of the option implies an added leverage for the counterparty by enhancing the yield and monetizing the benefit of embedded options.
Technical Characteristics
Unlike the standard interest rate swap, a range accrual swap is a instrument in which the payment of one of the legs depends on the daily fixings of an index being within a specific range. The interest received on each payment date is equal to:
when dfrac j is the day count fraction for the T j - T j-1 period, n j is the number of days during the observation period when the index fixes within the range (in relation to T j & T j-1 ) and N j is the total number of days in the observation period.
Note K could be a fixed rate, a money market rate or a swap rate.
Thus, if K is fixed, the net present value of the exotic leg has the form:
when df j is the discount factor at time T j.
Cap & Swaption Volatility
In a callable range accrual structure, two volatilities must be considered.
If the investor's coupon depends on the daily fixing of a money market rate, we first have to consider the volatility of a cap with, for example, three-month LIBOR as the underlying.
The higher the volatility of this index, the lower the probability the index will stay between the two barriers (for periods when the forward rates lie within the barriers)....