FYI

Vince

 -----Original Message-----
From: 	Lorenzo Pascual Caneiro <Lorenzo.Pascual.Caneiro@morganstanley.com>@ENRON [mailto:IMCEANOTES-Lorenzo+20Pascual+20Caneiro+20+3CLorenzo+2EPascual+2ECaneiro+40morganstanley+2Ecom+3E+40ENRON@ENRON.com] 
Sent:	Wednesday, July 25, 2001 12:46 PM
To:	vkamins@enron.com
Subject:	EPRM course

Dear Prof. Kaminski,

first of all, let me introduce myself. My name is Lorenzo Pascual and a
collegue of mine and I attended the Energy Power Risk Management
course that took place in London some weeks ago. About my CV,
I have finished a Ph. D. in Mathematics (Statistics and Econometrics) at
University Carlos
III in Madrid (Spain), as well as a master degree in Mathematical
Finance,
both of them two months ago. In particular, in my dissertation I have
developed
new statistical techniques (using bootstrap methods) for forecasting
returns and volatilities
in the GARCH and Stochastic Volatility family of models. I have already
one published
article at the International Journal of Forecasting, and I have three
more papers under
revision in other international journals. Of course, if you are
interested in this kind of
research I can send to you a copy of the working papers.
Since then, I work for Endesa Trading
(spanish electricity company based in Madrid). However, at this moment I
am based here
in London for two years working in a joint venture with Morgan Stanley.

During the course I had the pleasure to talk with you and you gave me
the opportunity of
asking you some of the questions and doubts I have about energy
derivatives.
We did not have enough time to discuss anything deeply so, you asked me
to send all
the questions by email.

If you are in London, it would be for me a pleasure to meet you here for
lunch some day and then
we could talk much better about everything. If you can not, it will be
ok to use the email.

I hope you can find some time to help me with this. Of course, I thank
you very much in
advance for your help because I understand you are very busy.

The main questions I need to be solved are the following:

1. This first question is very important because I want to know how to
use Monte Carlo
    methods for pricing all kind of options on the forward price when no
analytical formula
    is available. To understand the procedure I have compared the
analytical formula with
    the monte carlo results. For example, when the price follows the
geometric brownian
    motion I have programed the analytical
    expression for a call on the forward price (see attached file in
matlab: price_gbm.m)
    (which corresponds with formula 6.5 in the book) together with
    the monte carlo method proposed in your book with Clewlow and
Strickland (chapter 7,
    see attached file: price_gbmMC.m). In this case I achieve the same
results. However,
    if I try to do the same exercise when the underlying follows the
simplest mean reversion
    process (formula 6.6), I obtain very different results using formula
(6.12) in the book (I think there
    is a printing mistake on it) and the Monte Carlo techniques. I do
not really understand
    what might be happening. You suggested me to send to you the matlab
files to check them
    more carefully. The names are price_mr.m and price_mrMC.m for the
analytical and monte
    carlo respectively.

    2. Could it be possible to have some of the data sets you use in the
book to check if I achieve the
        same estimated parameters with my programs ? (estimacion_mbg.m
and estimacion_mr.m)

    3.. Once you have estimated the unknown parameters from the data
set, in
         particular the speed of mean-reversion,
         and, if you want to use the option formula under
mean-reversion,
         which is the value for this parameter
         to introduce in the formula, the annualized one or not?

4. In case I have to use the annualized value into the pricing
formula, I have a very important question which
   is driving my crazy.
   In the particular case of electricity price series, the estimated
annualized speed of mean reversion I obtain are really very high,
   and very far from zero. In this case, if you compare the pricing
values obtained using the usual black formula
   and the one obtained under mean-reversion, we achieve very different
values. Is that correct? Did you have similar results
   to mine when working with electricity series? (I computed these two
values under the same volatility).

5. Going back to the previous point, why do we have to use the spot
price volatility and not the forward volatility
   in the pricing formula?
   I do not understand why, since the underlying in this case is the
forward price.

6. If I compute the speed of mean-reversion for the same data set,
working with hourly data and with daily data (constructed
   as the sample mean of the hourly observations) I obtain very
different values for this parameter (for the annualized value). Is that
normal?
   Can be the different volatility values in these two series the reason

of that? Should not be both numbers very similar (the annualized ones of
course)?

7. If the estimated numbers we obtain for the speed of mean-reversion
have to be
different depending on the time between observations,
   has it sense the following question? : if the underlying of my
product is a monthly forward price, should I compute
   the speed of mean-reversion ( I mean the annualized value) with
monthly spot prices?
   In such a case, I expect to obtain a value closer to zero than in the

   other cases (with hourly and daily data) and then, I will obtain a
pricing value not as different
   to that obtained with the usual Black formula.

8. Finally, can you give me references (papers, working papers,...)
about who to value swing options ?

Thank you very much in advance. You can not imagine how much I
appreciate your answers. Looking forward to hearing from you.

Best regards,

Lorenzo Pascual.

 - estimacion_mr.m 
 - estimacion_mbg.m 
 - price_gbmMC.m 
 - price_gbm.m 
 - price_mrMC.m 
 - price_mr.m