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Function documentationInterest Rate Guarantees (OTC) Locate this document in the navigation structure

 

The market price calculator for interest rate guarantees (IRGs) calculates current market values, time values, and future market values (the future point in time is the horizon).

IRGs are options on forward rate agreements (FRAs) and come as either call or put. Both American and European exercise options are available. The buyer can set up an FRA at any time up to a particular date in the future (American), or on a specific date (European). If the horizon comes after the option term (or on the fixing date), there is no valuation of the IRG.

In valuing the IRG, the agreed fixed interest rate (Rf) of the FRA serves as the strike for the option. The IRG is regarded as an option on a forward interest rate (Rx), with the term and interest rate (Rf) fixed in the FRA. The user enters the interest volatility.

IRGs of the European type are valued using the Black-Scholes formula or the normal distribution model. American IRGs are valued using the binomial tree (with 30 or 31 periods).

Underlying:

You can create an FRA in all of its forms and variations as an underlying. However, only "classic IRGs" can be valued, that is, those with an underlying FRA whose fixing date is before or on the expiration date of the option. The option always ends on the fixing date of the reference interest rate of the FRA.

Integration

To value an IRG, the transaction data - or, alternatively, a par coupon or zero coupon yield curve - must exist in the transaction currency for the evaluation date. In addition, you need a yield curve to calculate the forward rate. You also need an interest volatility curve for the term of the option. The specified reference interest rate is the reference interest rate Rx used in the analysis. Zero bond discounting factors are calculated from the yield curve of the transaction currency. These, along with zero interest rates, can potentially be used for determining risk-free interest rates and discounting factors at a later date. You can use the zero coupon calculation method for this. The spot that later goes into the option price formula is also deleted. To do this, the forward calculator computes the forward rate for the agreed reference interest rate (Rx) in the FRA of the underlying. . If the transaction currency differs from the display currency of the IRG, the transaction currency is changed into the display currency using the currency rate from the horizon. If the horizon is later than the evaluation date, the corresponding forward currency rate is calculated for the evaluation date using the yield curves from the transaction and display currencies. The input parameters are calculated using function modules, such as the following:

Features

Depending on the type of option (American or European), the option price calculator uses the Black Scholes formula or the normal distribution model (for European options) or the binomial tree (for American options), along with the following values (some of which are taken from the input parameters):

  • Call/Put: Call/Put

  • Term: Term of the option in days (expiration date of the option to the horizon)

  • Spot: See input parameters

  • Strike: Comparative interest rate fixed in the FRA of the underlying

  • Interest rate 1: 0 (no forex option)

  • Interest rate 2: Risk-free interest rate = zero interest rate of the interest yield curve with a term equivalent to the option term.

  • Volatility: Interest volatility of the forward interest rate Rx from the volatility curve with a term corresponding to the option term

  • NPV: Net present value

The calculated result is the simulated value of the NPV of the interest rate difference DZ (on the horizon) between the forward reference interest rate Rx of the FRA and the strike on the expiration date of the option. The NPV of the IRG is then the interest difference (DZ) multiplied by the term (LZ) of the reference interest rate Rx (given in years) and the nominal volume (NV).

In addition to the formulas given already, the following are used:

NPV=K*DZ/100*NV*LZ

where

K: Call/Put indicator

If the display currency differs from the transaction currency, the NPV is calculated using the forward currency rate.