Subject: risk bucketing for P/L
From: [email-masked]
To: [email-masked], [email-masked]
Cc: [email-masked], [email-masked], [email-masked]
Date: Thu, 10 Aug 2000 10:26:00 -0700 (PDT)

Ken and Greg,

What we have been doing is absoutely fine under the assumption that the market
conditions move relatively small ( where Taylor series has fast convergence).
However, we could run into troubles when the market has a big move.

In order to have a error proof bucketing, we can use the following 
method(finite-difference), let me
know what you guys think how to implement it to the transport book.

Sensitivity to risk parameters, or P/L attribution by risk bucket:

Today's premium = Premium based on today's curves

Last day's premium = Premium based on last day's curves

Change due to
DeliveryCurveShift = [Premium based on today's delivery price and last day's 
receipt  price, volatilities, interest rate, last's time to expiration etc] - 
Last day's premium - today's change due to Gamma1

ReceiptCurveShift = [Premium based on today's receipt price and last day's 
everything else] - Last day's premium -today's change due to Gamma2

Vega1 = [Premium based on today's delivery volatility and last day's 
everything else] - Last day's premium

Vega2 = as above for gas volatility 

Rho =  as above for interest rate

Eta = as above for correlation

Theta = {[Premium based on today's days to expiration and last day's 
everything else] - Drift - Last day's premium } / 365.25

[This is a daily Theta.The sprdopt function returns an annualised theta.]

Gamma1 = 0.5 Last day's Gamma1' * PriceShift1 2??Gamma2 = 0.5 Last day's Gamma2' * PriceShift2 2

Drift = [(exp (Last day's interest rate*(Today - Last days) /365.25)) - 1 ]* 
Last day's premium

Priceshift1 = Today's delivery price - Last day's delivery price

Priceshift2 = Today's receipt price - Last day's receipt price

Gamma1' = theoretical Gamma1, i.e. gamma from spread option

Gamma2' = theoretical Gamma2, i.e. gamma from spread option calculation

Liquidation= Premium of option which expired the day before, i.e. intrinsic 
value.