A swaption is an option on an interest rate swap. There are numerous models for swaptions, Derivatives ONE uses Black’s 1976 model.
In addition to the black scholes inputs the model requires a Future Swap Rate (ie the future swap rate from the option maturity date to the swap maturity date) and the Risk Free Rate (ie the zero coupon government bond rate for the period from the valuation date to the swap maturity date).
Swaption Pricing
Interest Rate Swap Valuation
An Interest Rate Swap (IRS) is the exchange of a stream of floating interest payments in return for a stream of fixed interest payments. An interest rate swap consists of two legs, fixed rate and floating rate. The fixed rate leg payer pays a fixed rate (the Swap Rate) and receives a stream of floating payments. The floating leg payments are calculated at the prevailing market interest rate on that payment date, for example a floating leg with a payment frequency of Quarterly would have payments calculated using the current 3 month deposit rate on each payment date. (See Interest Rate Swap Example for a more detailed swap example)
Interest rate swaps are commonly used by both banks and corporates to convert interest payments. For example a corporation which issues floating rate bonds may wish instead to pay a fixed rate to enable financial planning. The corporate entering a pay fixed/receive floating swap would in effect convert that debt to fixed rate.
The fixed leg of the swap is typically the only leg which is sensitive to changes in interest rates as it can be considered as a fixed rate bond, the offsetting floating leg is typically insensitive to changes in interest rates as the rate refixes regularly throughout the life of the swap.
Derivatives ONE features a free valuation tool for Interest Rate Swaps.
Sign Up for Swap Valuation ToolsBasis Swap Valuation
A basis swap is the exchange of two floating rate interest streams of different payment basis. The different basis, can be either the payment frequency, day count or business day convention. As both streams are floating rate and therefore are relatively insensitive to changes in market interest rates , the streams have low NPV (net present values) and so basis swaps typically have minimal valuations (although different payment frequencies can lead to accrued interest balances).
Cross Currency Basis Swaps involve exchanging floating rate streams of different currencies These types of basis swaps are far more common as there is an intrinsic value to the swaps. The swaps can either have an exchange of notional on maturity or no exchange of notional, exchanging the notional on the maturity of the swap is the most common form as the swap is used to hedge an offsetting loan/investment which will be repaid on the maturity of the swap.
Derivative ONE features a free valuation tool for Basis Swap.
Sign Up for the Basis Swap Valuation ToolForward Rate Agreement (FRA) Valuation
A Forward Rate Agreement (FRA) is an interest rate forward purchase or sale contract.Under a FRA, the interest differential between the FRA contract rate and the market interest rate on the Settlement Date on the notional principal is paid or received.
In addition to the contract FRA rate valuation model requires the Future Rate (ie the futures interest rate from the settlement date to the final maturity date) and the Risk Free Interest Rate (ie the zero coupon government bond rate for the period from the valuation date to the final maturity date).