If I use fwd_price = S*(1+r_term)/(1+r_base) to determine the theoretical value of a forward, how should I tweak the formula to price a FX swap? Assuming swap = fwd-spot, swap_price = S*(1+r_term)/(1+r_base) - S or not?


Yes. The swap is quoted in fwd points relative to spot (sssuming that what you mean by r_term is the term interest rate of one currency and r_base the term interest rate of the other). Also, best to use market convention for the FX quotes.

  • $\begingroup$ Just to clarify, if you are long 1year EURUSD swap on 1mm of notional, how would you calculate the value/P&L of the position after inception? For example, at inception spot = 1.1000, fwd_rate = 1.1020 so 20 swap points, then say after 3 months spot = 1.1050, fwd_rate = 1.1080 so 30 swap points. $\endgroup$ – Student Dec 10 '20 at 15:30
  • $\begingroup$ After the initiation of the swap, you have a spot position and a fwd. If you are long 1mm EUR at 1.1 and spot is 1.105, you have gained 5000 on the near leg. On the far leg, you have sold 1mm EUR @ 1.102 or 1,102,000 one year out. To mark this fwd after 3 months, you would need the 9M fwd (assuming this is the 1.108) you have lost 6000 fwd (9M) dollars. Discount this by the appropriate rate and add the spot gain of 5000 to arrive at your PnL $\endgroup$ – AlRacoon Dec 10 '20 at 16:15
  • $\begingroup$ Ok! It would be equivalent to use swap points. PnL = N*(points_difference) or 1mm*(0.0030-0.0020) = 1000 loss, right? So in case you are long the spot and short the fwd it means you are short the points (our example), otherwise if you are short the spot and long the fwd you are long the points. It would be great to know what is the market convention, for example being long a EURUSD swap, does it mean long the spot and short the fwd or the other way around? Also is usually the notional expressed in the ccy you buy or sell in the sport leg? $\endgroup$ – Student Dec 10 '20 at 18:01
  • $\begingroup$ In EUR/USD the market convention is you are short Spot, long Forward. So the PnL will be reversed. Apologies. I am so used to it by the way I am typically positioned. Whenever I trade these or any other swap, I always clarify the positions rather than try to remember how market jargon. $\endgroup$ – AlRacoon Dec 10 '20 at 18:08
  • $\begingroup$ so if I say "I am long a EUR/USD swap", they understand short spot and long forward and "I am short a EUR/USD swap" the other way around ? $\endgroup$ – Student Dec 10 '20 at 18:20

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