Receivers swaption

The owner of a payer (receiver) swaption maturing at time To, has the right to enter at time To the underlying forward payer (receiver) swap settled in arreas (see e.g. Musiela and Rutkowski [61])... 

Now, we directly see that a swaption in general can be seen as an option on a coupon bond with strike K =1 and exercise date Tq paying the coupons q at the payment dates Ti = Ti. ..Tu. Armed with this, we obtain the price of a receiver swaption... 

As in section (5.2.2), we introduce the lEE technique by starting from a simpler model such that we obtain a closed-form solution for the option price. Then, the numerical approximations are directly comparable with the equivalent findings for the closed-form solution. Therefore, we derive the option pricing formula of a receiver swaption with only one (u = l) payment date in T. ... 

Before the lEE can be appUed to compute the price of a 1x1 receiver swaption we have to rewrite (5.31) as follows... 

A receivers swaption grants the holder the right to receive the fixed rate in the underlying swap. 

The buyer of this swaption has the right, one year from now, to enter into a 3-year swap as the fixed-rate payer, paying 4% p.a. against receiving 3-month EURIBOR, on a notional principal of 10 million. If 3-year swap rates on 29 March 20X4 were, say, 4.5%, it would be worthwhile for the owner to exercise the swaption, paying a fixed rate of only 4% when the market rate was 4.5%. 

If 2-year rates rise sufficiently in 3-years time, the swaption will expire in-the-money, and the investor can exercise the payer s swaption, entering into a second swap as the fixed-rate payer at exactly the same rate as the original swap, for which the investor is the fixed-rate receiver. This second swap exactly offsets the first swap, effectively cancelling the original swap for the last two years of its life. 

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