PelatihA cash-settled swaption pays, on exercise, the value of the underlying swap computed by an agreed method instead of delivering it. Under the par-yield method the value is with the cash annuity
the annuity of the swap discounted at its own par rate ( payments a year); under the collateralised-cash-price method it is the swap’s value on the discount curve of the agreed clearing house, as if physically settled.
Contoh
Example 4.8 (Five years into ten)
On chapter 2’s curves the ten-year swap starting in five years has a forward par rate of 3.098% against six-month Euribor and a (discount-curve) annuity of 7.740. At 80 basis points of normal volatility (a lognormal volatility of 26.2%), the at-the-money physical payer on EUR 100 million is worth EUR 5 525 150. The traditional cash formula, option, gives EUR 5 410 452, 2.1% less: , because the cash annuity discounts at the Euribor swap rate, above the €STR rates of the collateralised annuity. The par-yield payoff is also not a function of the annuity measure’s numeraire, so the formula is itself an approximation; the collateralised cash price removes both problems by settling at the physical value.