Message-ID: <25647427.1075863432767.JavaMail.evans@thyme> Date: Wed, 25 Jul 2001 13:02:45 -0700 (PDT) From: j.kaminski@enron.com To: kenneth.deng@enron.com Subject: FW: EPRM course Mime-Version: 1.0 Content-Type: text/plain; charset=us-ascii Content-Transfer-Encoding: 7bit X-From: Kaminski, Vince J X-To: Deng, Kenneth X-cc: X-bcc: X-Folder: \VKAMINS (Non-Privileged)\Kaminski, Vince J\Sent Items X-Origin: Kaminski-V X-FileName: VKAMINS (Non-Privileged).pst FYI Vince -----Original Message----- From: Lorenzo Pascual Caneiro @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