I'm doing a USD to INR fixed-to-fixed cross currency swap. The default curve has a fixed and a floating rate. However, the curve that I'm looking to use has floating rates on both legs. Would this curve be appropriate to use?
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1 Answer
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A pricing curve does not have legs.
A curve is a series of datapoints that defines either a discount factor (under some assumed model, e.g. USD cash collateral) for each business date, or a forecast interest rate (of some index e.g. 1M USD Libor).
Here is a curve:
GBP 3M Libor Forecast Rates: .. 13/Aug/19: 1.250%, 14/Aug/19: 1.252%, ..etc
Here is another curve:
GBP cashflows discounted under EUR Cash only CSA: .. 13/8/19: 0.99181, 14/Aug/19: 0.99112 ..etc
To NPV your fixed-fixed cross-currency swap you need to have the USD cashflows under a USD cash only CSA discount factor curve and the INR cashflows under a USD cash only CSA discount factor curve and, to equate the values in USD, the USDINR spot FX rate.
How you generate these curves is model dependent. Always, the USD cashflows under a USD cash only CSA discount factor curve is calculated by analysing USD Interest rate swaps (IRSs). To get the INR cashflows under a USD cash only CSA discount factor curve you would typically need the local INR IBOR forecast curve and INR discount curve, calculated from local INR IRSs or otherwise and then adjust the INR discount curve to suit the mid-market cross-currency swap prices.
It would not necessarily matter whether the cross-currency swap prices were float-float or fixed-fixed or fixed-float, so long as you are able to make correct adjustments to accomadate those correct market prices. Most curve models are constructed with float-float cross-currency swaps since they are most liquid in most markets.
