Options on Futures (Listed) 
Caution
The market price calculator for options on futures is used only in conjunction with sensitivity analysis, and the value-at-risk approach in Risk Analysis.
Options on futures are priced in the same way as futures, since these are also handled by using a margin account. This means that only change risks are displayed for future-style options.
Integration and calculation bases
To price tradable options, the transaction data, or a par coupon or zero coupon yield curve, have to provided in the transaction currency and for the evaluation date.
The relevant market data for the underlying (such as index values for options in stock index futures) has to be provided for valuing the options on futures.
If the display currency and the transaction currency of the option are different, then the relevant exchange rate is required. If the horizon is after the evaluation date, and the transaction currency is different from the display currency, then a par coupon or zero coupon yield curve has to be provided in the display currency (bid or ask rates) in order to calculate a forward rate for the end of the term.
The following methods are used to calculate the input parameters:
Scope of functions and valuation
The Black-Scholes model is used to price European options on futures.
The following parameters are used in the option price formula:
Strike of the option (depends upon the quotation type)
Spot of the underlying (corresponds to the future price)
– Securities price (for futures on fixed-rate securities)
– Forward rate (for futures on interest rates)
– Index price (for futures on indexes)
Volatility of the underlying of the option (for the term of the option)
– Volatility of the bond future (for futures on fixed-rate securities)
– Volatility of the forward rate (for futures on interest rates)
– Volatility of the index (for futures on indexes)
Dividends (for the products listed here, dividends are usually 0)
The system uses these input parameters to price the option to the horizon.
The premium for an option on a future is cleared in the same way as the underlying future contract. In accordance with the mark-to-market principle, options are settled daily (future style). This means that it is best to exercise the option on its maturity so that the option can be priced as a European option using the Black-Scholes model.
Since no option premium is paid when the option is purchased, the price of the future option has to be shown when the option matures.
The formula for pricing options on futures can be derived from the Black-Scholes formula for stock options, so that the stock price is replaced by the future price, and the short-term interest rate is set to zero. The short-term interest rate is irrelevant here because neither the underlying nor the option represents a capital commitment when a duplicate portfolio is generated.
Call = Future price x N(d1) – Strike x N(d2)
The rate is calculated based on the underlying as follows:
For options on an index future : Rate = number of contracts x index point value x future option
For options on an interest rate future : Rate = number of contacts x contract nominal / 100 x future option x M / 12 (M is the term of the underlying forward rate period in months).
For options on an bond future : Rate = number of contracts x contract nominal / 100 x future option
Note
The exchange rate risk of futures is always displayed as zero. If the evaluation currency and the transaction currency of the future are different, then the transaction is subject to currency risk only on the maturity date, as this is the first point in time when foreign currency is exchanged in return for the underlying. The currency risk on the margin account is ignored, as the clearing accounts are not part of the system.