Show TOC

 Option on Commodity Futures Locate this document in the navigation structure

Use

In this function, the following activities are possible:

  • You can create/change financial objects with active Analysis-Parts for class position in future accounts on commodity derivatives.

  • You can calculate the net present value (NPV) of a option on Commodity Future deal .

  • You can calculate the Clean Price of option on Commodity Future deals.

The market risk analyzer calculates the net present value of option on commodity futures using the Black 76 model.

Features

The market risk analyzer can calculate the net present value of still existing options on commodity futures. Class positions on future option accounts can only be calculated if the horizon is before the maturity of the option, and the maturity of the option is before the maturity of the underlying future. The price calculator calculates the net present value of existing options on commodity futures using the formula:

This graphic is explained in the accompanying text.

where NPV actual is the NPV calculated by using current market data, and NPV scenario is the NPV from scenario data.

Five steps are necessary:

  1. Determine the actual and scenario “future option price” ( ) and ( )

    ( ) and ( ) are calculated with actual market data or scenario market data in the same way, which will be described with general expressions “OptFut” and “market data”.

    The calculation of OptFutdepends upon whether the flag “calculate theoretical price” is set and whether the calling application delivers market data for the option on commodity future to the price calculator:

    If the flag is not set and market data for the option on commodity future are provided, then OptFutis equal to ( )

    If the flag is set, or no market data for the commodity future is provided, then OptFut has to be calculated theoretically.

    This calculation depends on the existence of market prices for the commodity future in the underlying:

    If market prices ( ) for the commodity future in the underlying exists, OptFut will be calculated on base of the existing prices:

    For European options use the Black model (black 76) :

    If no market prices ( ) for the commodity future in the underlying are given (or they are too old), OptFut will be calculated on the base of the prices for commodities in the underlying of the future.

  2. Calculate the theoretical value of the option of commodity future with actual market data ( NPV actual )

    Calculate NPV actua according to the formula

  3. Calculate the theoretical value of the option on commodity future with scenario / actual market data

    Calculate NPV scenario according to the formula

  4. Calculate the difference ( Δ NPV).

    Δ NPV = NPV scenario - NPV actual

  5. Convert the difference to reporting currency

    Convert ΔNPV to reporting currency

    Convert the difference in NPV scenario and NPV actual to the reporting currency, using the exchange rate from the market data.

When the scenario market data is equal to the actual market data, then the NPV calculations of options on commodity futures will equal zero, as the option future contract will have a margin call, and the profit or loss will be booked in the option futures account on the basis of daily market closing prices.

The market risk analyzer can calculate the clean price of options on commodity futures.

The clean price of the option on commodity futures is calculated using the following steps:

Calculate the clean price of the option on commodity future in position currency

Convert the value in reporting currency with the exchange rate and evaluation date

  1. Calculate the clean price of options on commodity futures by performing Step1 and Step 2 of the previous feature. Then the clean price ( ) is equal to ( ) .

  2. After the calculation of the clean price in position currency, it is converted to the reporting currency.

    The exchange rate (R) (forward rate on contract expiry) for the option buy/sell currency and the reporting currency has to be considered for conversion.

Delta for options on commodity futures will be calculated

According to the different possibilities for calculating the NPV / the clean price the calculation of the option delta depends on the existence of future prices for the underlying future, and the option type (European / American):

If future prices for the underling future exit:

If the option type is European, then delta is calculated by the formula

Delta (call) = ( )

Delta (Put) = ( ) -1

with

( ) ; ( )

If no future prices for the underling future exit, use spot prices and volatilities of the commodity as underlying of the underlying future:

If the option type is European, delta is calculated by the formula

Call option

This graphic is explained in the accompanying text.

Put Option

This graphic is explained in the accompanying text.

with

( ) ; ( )

For the first step we set the value of u and y to zero.

If the option type is American, calculate the clean price of the option twice with actual and shifted future prices and calculate delta using the formula

Delta = ( CP actual -CP Shift ) / Shift

The clean price calculation of listed options by theoretical value wouldfollow the analog way to the calculation by price.

Description:

The SAP calculation of the NPV and clean price of listed options with existing market prices is done according to the formulas

For options on index or stock:

This graphic is explained in the accompanying text.

For options on future:

This graphic is explained in the accompanying text.

This graphic is explained in the accompanying text.

with

NPV = Net Present Value (in position currency)

CP = Clean Price (in position currency)

PS = Position Size (Units in Position)

MP = Market price of option (with Actual/Scenario market data)

TV = Tick Value

TS = Tick Size.

To achieve a consistent calculation the NPV and clean price must be calculated using the same formula.

A theoretical price MP for the option must be calculated and inserted in the formula. This must be done for all existing option categories.