Whats Your Option?
By Brian Nicholson
BookRunner® provides for the valuation of a number of different option types. BookRunner® utilizes Financial Engineering Associates, Inc.'s (FEA) @Energy® software in valuing American, European, Asian and a variety of spread options. Delta, Gamma and other derived Greeks are also quantified by the software and reported on by BookRunner®. The @Energy software runs in the background as a compilation of calculation engines for valuation. The user will only interface with BookRunner®, which passes the parameters to the @Energy engine.
BookRunner® can value options on a monthly or daily basis. Option valuation inputs include the style of option, current commodity forward price, volatility estimates for forward prices, the strike price, interest rates for applicable currencies, applicable exchange rates, and the number of iterations to be used in valuing American options. Interest rates used by the model should be expressed as continuously compounded annual rates. Volatility estimates should be expressed as the annualized standard deviation of the underlying asset returns.
The following sections describe a variety of options that BookRunner® supports:
European Option
The European option is characterized by the inability to exercise the instrument prior to maturity. FEA's @Energy uses the Garman-Kohlhagen formula to value European options because of the model's robustness. Forward prices are passed directly into the model and used in obtaining the option's theoretical value.
It should be noted that any further calculations by the model, such as delta and gamma values, are recognized as forward delta and gamma values.
American Option
The American option is characterized by the ability to exercise the instrument any time prior to maturity. FEA's @Energy uses the Hull-White trinomial method to value American options. This model uses similar parameters and assumptions as the European pricing model. The trinomial model also requires the number of iterations to be performed in arriving at a value.
Asian Option
The Asian (average price) option is characterized by the underlying asset being an average value over a specified period. The option is exercised at the end of the averaging period, assuming it is profitable to do so. This model uses similar parameters and assumptions as the European pricing model.
An Asian option is the average of the daily settled prices for the averaging period. The option expires at the end of the averaging period and is valued accordingly. Within the averaging period, the system will calculate a running average of the daily prices or take the entered month price in valuing the option. The valuation engine will also take into account the number of days left in the averaging period before the index will settle. It should be noted that any further calculations by the model, such as delta and gamma values, are recognized as forward delta and gamma values.
American and European Swaption
American and European style swaptions are options on price swaps. The options have similar exercise characteristics as American and European options; however, the underlying asset is a fixed-for-floating price swap. Buying a call swaption gives you the right to purchase a swap. This implies you are purchasing the right, but not the obligation, to pay the fixed component of a fixed-for-floating swap. Buying a put swaption gives you the right to sell a Swap. This implies you are purchasing the right, but not the obligation, to receive the fixed component of a fixed-for-floating swap. A unique feature of this option is the ability for it to expire prior to the first fixing date of the swap. For example, the option on a swap commencing April 1st, 2006 may expire on Nov 1st, 2005.
The underlying swap is a term instrument that derives value from the expected value of the floating price index over the swap's term. The change in value of the swap is determined by the volatility of the float price index over the term of the swap. This implies that the change in value of an option on the swap is also largely determined by the volatility of the float price index. As a result, the correct volatility assumption to use when valuing the swaption is the expected volatility of the float price index over the term of the swap from the current date to the expiry of the option. This requires a unique term volatility to be used for option valuation. It should be noted that any further calculations by the model, such as delta and gamma values, are recognized as forward delta and gamma values.
Asian Spread Option
An Asian spread option is an option where the underlying asset is the average differential of two assets during the same averaging period (where the average fixing dates of the two assets are identical).
Calendar Spread Option
A calendar spread option is similar to a spread option where the price differential is between the two-futures/forward contracts with different maturities on the same underlying asset. A calendar spread is an option on a strip of months, such as an option on winter and summer gas spreads.
The calendar spread option creates two exposures on two different dates and Greek values are read from corresponding Delta, and Gamma curves (there are no delta2, or gamma2 values, instead there is a second delta point on the same delta curve, and a second gamma point on the same gamma curve).
Crack Spread Option
A crack spread option is an option on the price differential between three underlying assets where the weights of the assets have mixed signs (for example, +3, -2, -1) and are netted together for a single basket value, which settles against the option's strike price. The option expiry for a crack spread option defaults to the option expiry calculated by the system for the first underlying index's option expiry date.
For more information concerning this article, please contact Brian Nicholson at bnicholson@riskadvisory.com , or by calling 403 263 7475.