The market price calculator for swaptions calculates current market values. It also calculates market values and time values for a future point in time (horizon).

A swaption, depending on the underlying transaction, is usually an option on an interest rate swap with a purely fixed side and a purely floating side. It comes in the varieties call and put. Currently, only the European type can be processed. Under the conditions for a European swap, the buyer has the right to make a swap on a given date. Only swaptions will be valuated whose expiration comes after the horizon.

To valuate a swaption, the swap is divided into a fixed-rate bond (fixed side) and a floating-rate bond (floating side). The swaption is then valuated like an option on the fixed-rate side with a strike of 1 using the option price formula from Black (for European type). The price volatility of the fixed side of the swap is approximated from the interest volatility using the duration and the yield.

Currently, it is only possible to use an interest rate swap with a purely fixed side and a purely floating side as the underlying security. You can have a swap as an underlying with the charateristics fixed rate payer and fixed rate receiver swaps.

To valuate a swaption, you need to enter the transaction data and either a par coupon or zero coupon yield curve in the transaction currency (bid or ask rate) for the evaluation date.

You will also need an interest rate volatility curve for the option terms. The specified reference interest rate is the reference interest rate from the yield curve (set up in the evaluation type) whose term is closest to the term of the fixed side of the swap.

If the display currency differs from that of the transaction currency, you will need the relevant exchange rate. If the horizon comes after the evaluation date and the transaction currency differs from the display currency, then you have to enter a parcoupon or zero coupon yield curve so that the forward exchange rate can be calculated for the horizon.

Depending on the calculation routine, the following input parameters are calculated for later use in determining the risk-free interest rate and for calculating the spot (both go into the option price formula).

• Zero coupon rates and zero bond discounting factors

• Spot:
  
  The spot is the NPV (on the horizon) of the absolute price (standardized to nominal volume) of the fixed side of the swap at expiration. Treasury Management automatically generates a cash flow for the fixed side of the swap when it is created. The cash flow consists of interest payments and principal payments which fall on certain dates. Both the due dates and amounts of the individual cash flows is known. Depending on the calculation method (par or zero coupon method), the NPVs of the individual cash flows are calculated on the horizon using the yield curves corresponding to the transaction currency of the fixed side. The value of the money market transaction (in transaction currency) is then the sum of the NPVs of the cash flows.
  
  Note the following definitions:

• t_i: Expected cash flow dates
• C_i: Cash flow at time t _i
• NPV(C_i): NPV of the cash flow on the horizon, due in t _i
• NV: Nominal volume of swap

• Volatility:
  
  The interest volatility is calculated from the interest volatility curve according to the difference between the term of the option and the horizon (possibly linearly interpolated). Then, using the modified duration (related to interest and principal cash flows from the fixed side of the forward swap) and the forward zero yield for the term of the swap (calculated from given zero bond discounting factors), the interest volatility is converted to a price volatility by the price volatility calculator.

• Call/put indicator:
  
  If the swap in the underlying transaction of the swaption is a fixed-rate receiver swap, the swaption can be viewed as a call on the fixed side of the swap. The call/put indicator is set to call. If the swap in the underlying transaction of the swaption is a fixed-rate payer swap, the swaption can be viewed as a put on the fixed side of the swap. The call/put indicator is set to put.

If the display currency differs from that of the transaction currency, the exchange rate on the horizon is used to convert from the transaction currency into the display currency. If the horizon comes after the evaluation date, the forward exchange rate will be calculated from the exchange rate on the evaluation date using the yield curves from the transaction and display currencies.

The option price calculator for pricing European options (Black-Scholes formula) is called up with the following parameters:

• Call/put: see input parameters
• Term: Term of the option in days (expiration of the option - horizon)
• Spot: see input parameters
• Strike: 1 (the value of the variable side of the swap approximating the nominal volume)
• Interest rate 1: 0 (no currency option)
• Interest rate 2: risk-free interest rate = zero interest rate of the given yield curve term which is the same as the option term.
• Volatility: see input parameters

The NPV of the swaption (in transaction currency) is the interest difference (DZ) multiplied by the nominal volume (NV).

We end up with the following formula:

with:

B: Buy/sell indicator

If the display currency differs from the transaction currency, the NPV is converted using the (forward) exchange rate.