Subject: P+ option valuation model
From: [email-masked]
To: [email-masked]
Cc: [email-masked], [email-masked]
Date: Wed, 11 Apr 2001 07:30:00 -0700 (PDT)

Mark,

After recently reviewing the booking of the P+ options, it is my 
understanding that these options are being valued using a standard spread 
option model where the price evolution of the two legs of the spread are 
assumed to be correlated Geometric Brownian Motion processes  (i.e. the price 
process assumptions are consistent with standard Black-76 model assumptions 
extended to two commodities).  

The payoff for a call option is:

Payoff = Max( 0,  A ) B ) K).

Where:
 A = NXWTI (delivery price for Nymex)
 B = Posting Price = (WTI Swap) ) (Posting Basis)
 K= Posting Bonus (fixed).

The only complication of this option as compared to most other spread options 
is that leg "B" of the spread is a combination of three prices,  the two 
futures prices which make up the WTI swap for the given month, and the 
average posting basis during the delivery month.   Combination of these 
prices is easily addressed by simply setting the volatility of leg "B" and 
the correlation to correctly account for the volatility of this basket of 
prices and its correlation with the NXWTI price.  I believe that this 
approach is more straightforward than the alternative, which would be to use 
a three or four-commodity model with its associated volatility and 
correlation matrices.

In summary, I believe that this is an appropriate model for valuation of 
these types of options, assuming that the inputs are set correctly.

Regards,

Stinson Gibner
V. P. Research