Swaption

Swaptions are options that allow the buyer to the payment of a single premium, at any given time ( European swaption ), up to a certain point ( American swaption, extremely rare) or at fixed consecutive time points ( Bermuda swaption ) into an interest rate swap to enter. The swap is fixed in terms of its maturity and interest rate.

Types of swaptions

A distinction is made between swaptions and receiver swaptions:

  • Receiver swaption (rarely sometimes also called call swaption ): The buyer of a swaption receiver has the right to enter into a swap in which it receives a fixed interest rate and pays a floating interest rate. The receiver swaption is a hedge against falling interest rates.
  • Payer swaption (rarely sometimes also called the put swaption ): The buyer of a swaption Payer has the right to enter into a swap in which it pays a fixed rate and receives a variable interest rate. The payer swaption is a hedge against rising interest rates.

The terms "call" and "put" - swaption are rather uncommon in practice and use in the literature is inconsistent.

Exercise of swaptions

When swap Settlement ( or Physical Settlement ) occur buyer and seller of the swaption, if exercised in an interest rate swap one.

In cash settlement, the seller pays the buyer the present value of interest rate swaps. This is calculated by discounting the difference between the agreed fixed rate (strike of the swaption ) and the date the swap market traded fixed rate (current swap rate ). In the euro area there By convention before, discounted at the current swap rate, ie no discounting at the interest rate curve.

Option pricing

One of the most popular models for the evaluation of European swaptions is the classic model of Fischer Black from the year 1976. It is precisely because of the ease of understanding and ease of implementation are still very popular. The model was originally developed by Fischer Black and Myron Scholes in Samuel named after them Black-Scholes model in 1973, for the valuation of stock options and assumed log- normally distributed stock prices. By applying this model to the valuation of swaptions acceptance of the lognormal distribution of stock prices is transmitted to the changes in the swap rate.

The price of a payer swaption with cash settlement is as follows:

The price for a receiver swaption with cash settlement is as follows:

With:

  • = Term of the swap (in years)
  • = Forward rate of the swap
  • = The strike, that is, the contractually agreed fixed rate of the swap
  • = Risk -free interest rate
  • = Maturity of the option (in years until exercise )
  • = Implied volatility of the forward rate of the swap
  • = Payment frequency of the fixed rate (1 = annual, 2 = semiannual )
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