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As OTC instruments, interest rate swaps (IRSs) can be customised in a number of ways and can be structured to meet the specific needs of the counterparties. For example: payment dates could be irregular, the notional of the swap could be amortized over time, reset dates (or fixing dates) of the floating rate could be irregular, mandatory break clauses may be inserted into the contract, etc.
To derive this rate we observe that the theoretical price of a bond can be calculated as the present value of the cash flows to be received in the future. In the case of swap rates, we want the par bond rate (Swaps are priced at par when created) and therefore we require that the present value of the future cash flows and principal be equal to ...
Other common pricing-methods are simulation and PDEs. Option-adjusted spread (OAS) is the yield spread which has to be added to a benchmark yield curve to discount a security's payments to match its market price, using a dynamic pricing model that accounts for embedded options. OAS is hence model-dependent.
In the context of an interest rate swap, the notional principal amount is the specified amount on which the exchanged interest payments are based; this could be 8000 US dollars, or 2.7 million pounds sterling, or any other combination of a number and a currency. Each period's rates are multiplied by the notional principal amount to determine ...
Lattices are commonly used in valuing bond options, swaptions, and other interest rate derivatives [24] [25] In these cases the valuation is largely as above, but requires an additional, zeroeth, step of constructing an interest rate tree, on which the price of the underlying is then based. The next step also differs: the underlying price here ...
For discounting, the overnight indexed swap (OIS) curve is typically used for the "risk free rate", as opposed to LIBOR as previously; see Interest rate swap § Valuation and pricing. Relatedly, the "Multi-curve framework" is now standard in the valuation of interest rate derivatives and for fixed income analysis more generally.
A Credit valuation adjustment (CVA), [a] in financial mathematics, is an "adjustment" to a derivative's price, as charged by a bank to a counterparty to compensate it for taking on the credit risk of that counterparty during the life of the transaction. "CVA" can refer more generally to several related concepts, as delineated aside.
The valuation of swaptions is complicated in that the at-the-money level is the forward swap rate, being the forward rate that would apply between the maturity of the option—time m—and the tenor of the underlying swap such that the swap, at time m, would have an "NPV" of zero; see swap valuation. Moneyness, therefore, is determined based on ...