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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.
The forward values of the overnight rate can be read from the overnight index swap curve. "OIS-discounting" is now standard, and is sometimes, referred to as "CSA-discounting". See: Financial economics § Derivative pricing for context; Interest rate swap § Valuation and pricing for the math.
While this principle holds true for any swap, the following discussion is for plain vanilla interest rate swaps and is representative of pure rational pricing as it excludes credit risk. For interest rate swaps, there are in fact two methods, which will (must) return the same value: in terms of bond prices, or as a portfolio of forward ...
The same approach is used in valuing swaptions, [4] where the value of the underlying swap is also a function of the evolving interest rate. (Whereas these options are more commonly valued using lattice based models, as above, for path dependent interest rate derivatives – such as CMOs – simulation is the primary technique employed. [5])
Since the 2007–2008 financial crisis, swap pricing is (generally) under a "multi-curve framework", whereas previously it was off a single, "self discounting", curve; see Interest rate swap § Valuation and pricing.
This concept can be applied to a mortgage-backed security (MBS), or another bond with embedded options, or any other interest rate derivative or option. More loosely, the OAS of a security can be interpreted as its "expected outperformance" versus the benchmarks, if the cash flows and the yield curve behave consistently with the valuation model.
A zero coupon swap (ZCS) [1] is a derivative contract made between two parties with terms defining two 'legs' upon which each party either makes or receives payments. One leg is the traditional fixed leg, whose cashflows are determined at the outset, usually defined by an agreed fixed rate of interest.
The Black model (sometimes known as the Black-76 model) is a variant of the Black–Scholes option pricing model. Its primary applications are for pricing options on future contracts, bond options, interest rate cap and floors, and swaptions. It was first presented in a paper written by Fischer Black in 1976.