Editing Rational pricing (section)

===Swaps===
Rational pricing underpins the logic of [[Swap (finance)|swap]] valuation. Here, two [[Counterparty|counterparties]] "swap" obligations, effectively exchanging [[cash flow]] streams calculated against a notional [[:wikt:principal|principal]] amount, and the value of the swap is the [[present value]] (PV) of both sets of future cash flows "netted off" against each other. 

To be arbitrage free, the terms of a swap contract are such that, initially, the [[Net present value|''Net'' present value]] of these future cash flows is equal to zero; see {{slink|Swap (finance)#Valuation and Pricing}}.  Once traded, swaps can (must) also be priced using rational pricing. 

The examples below are for [[interest rate swap]]s{{snd}} and are representative of pure rational pricing as these exclude [[credit risk]]{{snd}} although the principle applies to [[:Category:Swaps (finance)|any type of swap]].
<!-- Note that since the [[2007–2012 global financial crisis]], pricing is under a "multi-curve" framework, whereas previously it was off a single, "self discounting", curve; see [[Financial economics#Derivative pricing]] for context. Of course, under both approaches, pricing must be arbitrage free, and the logic below therefore holds under either, although see [[Interest rate swap#Valuation and pricing]] for formulae. (not arbitrage related, and therefore confusing...)-->

====Valuation at initiation====
Consider a fixed-to-floating Interest rate swap where Party A pays a fixed rate ("[[Swap rate]]"), and Party B pays a floating rate. Here, the ''fixed rate'' would be such that the present value of future fixed rate payments by Party A is equal to the present value of the ''expected'' future floating rate payments (i.e. the NPV is zero). Were this not the case, an arbitrageur, C, could:
# Assume the position with the ''lower'' present value of payments, and borrow funds equal to this present value
# Meet the cash flow obligations on the position by using the borrowed funds, and receive the corresponding payments—which have a higher present value
# Use the received payments to repay the debt on the borrowed funds
# Pocket the difference&nbsp;– where the difference between the present value of the loan and the present value of the inflows is the arbitrage profit

====Subsequent valuation====
The Floating leg of an interest rate swap can be "decomposed" into a series of [[forward rate agreement]]s. Here, since the swap has identical payments to the FRA,  arbitrage free pricing must apply as above&nbsp;– i.e. the value of this leg is equal to the value of the corresponding FRAs. Similarly, the "receive-fixed" leg of a swap can be valued by comparison to a [[Bond (finance)|bond]] with the same schedule of payments. (Relatedly, given that their [[underlying]]s have the same cash flows, [[bond option]]s and [[swaption]]s are equatable.)  See further under {{slink|Swap (finance)#Using bond prices}}. The difference between the [[Interest rate cap and floor]] values equate to the swap value, per similar arbitrage arguments.