What's the difference between a payer and receiver swaption, and how are they valued?

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AcadiFi · Accepted Answer

A payer swaption gives the holder the right to enter a swap paying fixed and receiving floating—valuable when rates rise above the strike. A receiver swaption gives the right to receive fixed and pay floating—valuable when rates fall below the strike.

Using Black's model, a payer swaption is priced as: PVBP * [SR*N(d1) - K*N(d2)] where SR is the forward swap rate, K is the strike swap rate, and PVBP is the present value of a basis point over the swap tenor. A receiver swaption uses: PVBP * [K*N(-d2) - SR*N(-d1)].

For Helix's 2-into-5 payer swaption (2-year expiry into 5-year swap) with SR = 4.5%, K = 4.25%, sigma = 20%, PVBP = 4.2: d1 = [ln(4.5/4.25) + (0.04/2)(2)] / (0.20*1.414) = 0.344, N(d1) = 0.635. d2 = 0.061, N(d2) = 0.524. Value = 4.2 * [0.045(0.635) - 0.0425(0.524)] = 4.2 * [0.02858 - 0.02227] = 0.0265 per $1 notional, or $265,000 per $10M.

Payer swaptions hedge rising rate exposure (floating-rate borrowers, callable bond issuers). Receiver swaptions hedge falling rate exposure (pension funds with fixed liabilities, putable bond holders). Put-call parity for swaptions: Payer - Receiver = Forward Swap Value.

What's the difference between a payer and receiver swaption, and how are they valued?

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