What is the exact details of swap option whose PV gives the counterparty exposure at horizon of t=15months for a payer swap of strike 1% above ATM and length 5y starting at 2y?


What you are describing is a payer swaption expiring in 15 months, with the strike being 1% above the current at the money forward swap rate for a forward starting swap where the swap starts 2yrs from now and ends 7 years from now (a 5 year forward starting swap).

The buyer of the payer swaption will exercise the swaption if at maturity in 15 months, the forward swap rate for a 5 year swap starting in 9 months and ending in 5years and 9 months is greater than the strike agreed on trade date. The terms of the underlying swap agreed to at trade date rolls down during the term of the swaption.

If exercised, they will enter into a forward starting swap where they will pay fixed strike rate (semi annually) and receive the floating rate (3M Libor) starting in 0.75 years and ending in 5.75 years from exercise date. Alternatively this can be cash settled at exercise for the then PV of that swap.

The counter party exposure is the value of that option if you are the buyer.

  • $\begingroup$ Thanks AIRacoon. So the Swanton PV will be calculated as of today(t0) using Black Swaption formula A* BlackPayer(F, K, t_ex, v) with t_ex=t=15months, F=current swap rate i.e. F(t0, t, t+5y), K=F(t0, ts=2y, te=7y)+1%, $\endgroup$ – babyQuant Nov 4 '19 at 15:36
  • $\begingroup$ F will be the forward swap rate also for the Swap starting in 2Y and ending in 7 years. $\endgroup$ – AlRacoon Nov 4 '19 at 15:55
  • $\begingroup$ Thanks AIRacoon, We have ts=2y, L=5y, quarterly coupons & fixings and t0= today. As per your reply the exposure of swap(ts, L, K) for ensure dare t=15months will be: Annuity(t0, t, t+L) * Black(F,K,t,v) Where, Annuity = 0.25*[DF(t0,t+3m) + DF(t0,t+6m) + … + DF(t0,t+L)]; First input to Black: F = F(t0, t, t+L) Second input: K is same as swap whose exposure we are calculating. Third input :Time to expiry = t = 15 months. Fourth input: vol is of a swap of length L and term = t = 15 months. $\endgroup$ – babyQuant Nov 4 '19 at 16:40
  • $\begingroup$ And then there will be a case with t>ts, i.e one or more fixings have occurred. $\endgroup$ – babyQuant Nov 4 '19 at 16:42

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