Analyzing the equivalence between swaptions and swaps in Layman’s terms…

A swaption is a derivative that provides the option, but not the obligation, to enter into a swap agreement. Specifically, a receiver swaption allows the holder to enter into a swap where they receive a fixed rate and pay a floating rate. This can be particularly useful for financial institutions like banks, which often need to manage interest rate risks.

For example, consider a bank that makes loans at floating rates and is concerned about future declines in interest rates. To hedge this risk, the bank could enter a swap where it receives a fixed rate and pays a floating rate. In this scenario, the bank benefits if the floating rate falls below the fixed rate, as it would pay less (the lower floating rate) and receive more (the fixed rate).

However, the bank might choose a different approach: going long on a receiver swaption and short on a payer swaption, both with the same exercise rate. Let’s say the swaption has a three-month expiry and gives the right to enter a swap at a 4% fixed rate.

In the first scenario, if the floating rate at expiry is 5%, the holder of a long position in a receive-fixed, pay-floating swap would receive 4% and pay 5%, resulting in a -1% payoff. The holder of the receiver swaption wouldn’t exercise their right, as they would be receiving a lower fixed rate and paying a higher floating rate, leading to a zero payoff (excluding the premium). The long payer swaption holder would exercise their right, leading the short payer swaption party to receive 4% and pay 5%, also resulting in a -1% payoff.

In the second scenario, if the floating rate is 3% at expiry, the holder of the receive-fixed, pay-floating swap receives 4% and pays 3%, a +1% payoff. The receiver swaption holder exercises their right for the same payoff, while the payer swaption holder does not, leaving the short payer swaption party with the premium only.

In both scenarios, the combined position of holding a long receiver swaption and a short payer swaption mirrors the payoff of a long receive-fixed, pay-floating swap. This demonstrates the equivalence of these positions under different interest rate scenarios. When rates fall below the exercise rate, the bank effectively converts its floating rate loans to fixed rate, thus achieving its hedging goal.

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