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

A floor contains a number of ways to guard against a reference interest rate R_x from falling below a fixed value R _x (strike). If the floor's term begin comes before the horizon, it contains an existing fixed-interest transaction on the horizon. The value of the reference interest rate R _k is set at fixed intervals of length t (e.g. every six months). If at time point k t the value of the reference interest rate R _k is below the agreed upon interest rate R _x, the buyer of the cap is paid the difference at time point (k + 1) t.

Generally for floors where

• R_x: Floor rate
• L: Nominal value
• Z: interest payments at time points t, 2 t, ¼, n t,

it is the case that the seller of the floor has to make the following payment at time point (k+1)t:

Assuming that F_k is the forward rate for the time frame between k t and (k+1) t, and that interest rates R _x, R _k and F _k are all expressly related to compounding frequency t, you can assume an approximation of F _k as the discount rate for the time frame between k t and (k + 1) t. This would mean that the above described payment at time point (k+t) t is equivalent to the payment of

at time point Kt. The advantage to this way of looking at things is that it allows every floorlet to be viewed as a call on a t-periodic interest rate, where payment is made when the option expires and not a period later. The nominal value of the underlying for every option is:

To valuate a floor or an individual floorlets, 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. In addition, a yield curve also has to be specified for calculating the forward rates F_k. If the term begin of the floor related to the evaluation day is in the past, then interest rate Rf for the fixing has to be specified for the current floorlet. If this interest rate is not available, the value of the interest rate is set to 0.

You will also need an interest rate volatility curve for the option terms. The specified reference interest rate is the observed reference interest rate Rk.

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.

To valuate a floor or an individual floorlets, 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. In addition, a yield curve also has to be specified for calculating the forward rates F_k. If the term begin of the floor related to the evaluation day is in the past, then interest rate Rf for the fixing has to be specified for the current floorlet. If this interest rate is not available, the value of the interest rate is set to 0.

You will also need an interest rate volatility curve for the option terms. The specified reference interest rate is the observed reference interest rate Rk.

First, the floor is reduced to the individual floorlets which expire after the horizon.

Zero bond interest rates and zero bond discounting facts are calculated from the yield curve of the transaction currency to later determine risk-free interest rates (the ones used in option price formulae for individual floorlet), and to determine the discounting factors of the current floorlet on the horizon.

The spot rate is calculated for each floorlet, and later flows into the option price formula.

For each floorlet whose term begin comes after the horizon, the option price calculator for pricing European options (Black-Scholes formula) is called up with the following parameters:

• Call/put: Call
• Term: Term to the beginning of the caplets (is the term of the corresponding option) in days (beginning of the caplet - horizon)
• Spot: see input parameters
• Strike: Comparative interest rate R_x in cap
• Interest rate 1: 0 (no currency option)
• Interest rate 2: risk-free = zero bond interest rate of the given yield curve structure with term equal to the beginning of the floorlet.
• Volatility: Interest volatility of reference interest rate R_k from the volatility curve with term equal to that of the caplet.

The following procedure is used to calculate the option value:

The result is simulated. It is the NPV on the horizon of the difference (DZ) between the reference interest rate R_k an the strike R _x on the date the option expires (i.e. at the start of the floorlet).

The NPV of the floorlet (in transaction currency) is then the DZ multiplied by the nominal volume.

We end up with the following formula:

with:

B: Buy/sell indicator

The NPV of the floorlet current on the horizon is also calculated (in transaction currency). If the term begin of the floorlet comes before the evaluation day, the NPV of interest difference (minimum = 0) from the fixed interest rate and the floor rate is calculated on the horizon (using transaction currency of current floorlet), and multiplied with the nominal volume (NV) and compounding frequency (t). If the term start of the floorlet comes after the evaluation date, the forward rate F_k will be calculated from the reference interest rate R _k using the forward calculator. The NPV of interest difference (minimum = 0) between the calculated forward rate F _k and the floor rate is calculated on the horizon (using transaction currency of current floorlet), and multiplied with the nominal volume (NV) and compounding frequency (t).

We end up with the following formula:

• If the term begin of the floorlet < evaluation date:

• If the term begin of the floorlet > evaluation date:

with:

B: Buy/sell indicator

The NPV of the floor is then the sum of the NPVs of the individual floorlets. We end up with the following formula:

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