Show TOC

 Using the Hull-White Model to Price Interest Rate Options Locate this document in the navigation structure

Use

You can use the Hull-White model to price options on interest rate instruments. This model is based upon the assumption that the variance of the underlying is limited even for transactions with long terms. This is a realistic assumption where the underlying is an interest rate, which means that the Hull-White model is used in preference to the Black-Scholes model for pricing interest rate instruments.

Integration

In the SAP system, you can use either the Black-Scholes model or the Hull-White model to price European interest rate options. The Hull-White model is provided for the pricing of American-style interest rate options.

If you want to price interest rate options using the Hull-White model, then you specify this model in the Customizing for the valuation rule. You can also use the Black-Scholes model to price European swaptions as interest rate options.

Prerequisites

You need to have already created a valuation rule in which you defined that the Hull-White model is to be used as the valuation model. To define a valuation rule, in the Customizing for Risk Analysis choose   Common Settings for Market Risk and ALM   Valuation   Valuation Rule.   To assign the valuation rule to an evaluation type, in the Customizing for Risk Analysis choose   Common Settings for Market Risk and ALM   Valuation   Define Evaluation Type.  

Features

The Hull-White model prices both European and American interest rate options. European-style options are priced using analytical formulas; American-style options are priced using the trinomial tree method. Since the calculation methods have been designed for OTC options on fixed-rate transactions, the system maps the underlying transactions to fixed-rate transactions before applying the calculation methods.

Preparation

The system first maps the underlying instruments to fixed-rate transactions. The following rules apply in this process:

  • All underlying instruments have to be created in the SAP system as long transactions. The initial cash flow resulting from the purchase of the instrument is negative; the cash flow resulting from the sale of the instrument on its maturity is positive.

  • The cash flows resulting from the initial purchase of the instrument, and the discounts and premiums, are not included in the valuation.

  • The price calculator needs the strike price as a price, and not as an interest rate. The strike price must be given as a clean price; when options are exercised in the time period between the start and the end of the fixed-rate period, accrued interest is not taken into account in the strike price. In the valuation process, the system converts the strike price from a clean price to a dirty price.

The underlying is handled as follows:

  • Fixed-rate transactions (all OTC transactions with fixed rates)

    The cash flows are transferred as they are, and are not changed.

  • Bonds (all fixed-rate securities)

    The cash flows are scaled to the amounts that flow when the option is exercised. The subscription ratio is used as the factor. (For example, for an option on ten bonds, the cash flows of the bonds are multiplied by ten).

  • Swaps

    The system handles swaps as follows:

    • The floating side of the swap is removed; any spreads it contains are valued as fixed-rate payments, and these values are then used in the calculation.

    • Cash flows arising from the sale of the swap, and changes in the nominal value of the fixed side are used in the calculation. This also applies for cash flows that, strictly speaking, do not flow in reality.

    • In the case of payer swaptions, the plus/minus sign of all the cash flows of the basic instrument are reversed. The system converts the signs so that the underlying instrument is available for the step in which the transaction is valued as a long position. (In the case of a payer swaption, when the option is exercised the holder of the option pays the fixed-rate interest, and receives the floating part.)

    • In payer swaptions, the put/call indicator is set to put ; in receiver swaptions it is set to call .

    • If the exercise date is at the start of an interest period of the floating side, or falls within such a period, then the strike is set to the nominal amount of the current interest period of the floating side. Otherwise the nominal amount of the swap is taken as the strike price.

  • Caps and floors

    If the underlying is a cap or a floor, the system prices the transaction as follows:

    • The cap is broken down into caplets, and the floor into floorlets.

    • If the interest period of the caplets and floorlets starts on or before the evaluation date, then the interest rate is already fixed. They are then priced by discounting the relevant cash flows.

    • Where this is not the case, the caplets and floorlets are priced as European options on a fixed-rate transaction. They have one interest period, and the interest rate is the same as the cap rate. In the case of a caplet, the put/call indicator is set to put ; for floorlets it is set to call .

    • The nominal amount is taken as the strike price.

Valuation

For more information about the pricing methods see Using the Hull-White Model to Price Options .