Seasonal commodity modelling - MM or HJM?

easy · December 10th, 2007, 4:11 pm

Does anyone have any strong views on what is the better framework for modelling seasonal commodities, a market model where the covariances are conditioned on historical behaviour and then calibrated to market, or an HJM approach with an embedded Fourier series and mean reversion? One argument against the market model is that it suffers if there's no historical data, while HJM doesn't separate correlation and vols.

yabbadabba · December 10th, 2007, 6:37 pm

I'd like to throw in a third alternative, namely using wavelets. See e.g. Wavelets in Economics and Finance: Past and Future, James B. Ramsey, New York University

jd1123 · December 11th, 2007, 10:38 am

Interesting question. For which commodity would you being doing this?

easy · December 11th, 2007, 11:30 am

This is motivated by the need to model natural gas forward curves, rather than spot prices, but am thinking that corn or wheat could be done in the same framework.

nparaschos · December 11th, 2007, 6:28 pm

I use a HJM with PCA (to reduce the dimensionality of the correlation matrix) to model NG futures prices. I've tried it with power curves and it works well but the price history first requires some de-seasonalizing.

easy · December 11th, 2007, 8:59 pm

Do you have seasonal correlation matrices and do you attempt to calibrate the model to the implied vols, or are you happy to run with historical?I have looked at the parametric HJM approach (I had a paper by Blix which I can't find online these days) and thought a summer and a winter model would suit the market better than one model for the curve. That led me to the market model approach with seaosonal historic covars.

nparaschos · December 18th, 2007, 5:51 pm

I'm thinking about it but am not too sure yet whether seasonal correlations would increase accuracy a great deal...I DO need to take a closer look though. As far as vols, power implied vols for ERCOT and NEPOOL are extremely hard to come by. For NYMEX gas of course that's quite easy.

gjlipman · December 19th, 2007, 8:41 am

nparaschos, do you have any good articles that go through the PCA approach for commodities? Also, how do you treat the fact that seasonality itself may change?

nparaschos · December 21st, 2007, 4:05 pm

I have mainly relied on Jon Frye's Principals of Risk and some of Borovkova's work (both attached).Isn't seasonality change reflected in the volatility curves? If yes, then the seasonal premia used in de-seasonalising the forward curve would account for that. In this manner the seasonality is calculated as the deviation of each average futures month (from historical data) from the current level of the futures month.

gjlipman · December 23rd, 2007, 12:59 pm

Thanks for those articles.The approach taken in the Borovova article assumes that the seasonality premia are deterministic - I'm not comfortable in making that assumption, and feel that it signficantly impacts the value of calendar spread options. I read a good article by Blanco and Stefiszyn (Valuing Natural Gas Storage Using Seasonal Principal Component Analysis) that talked through one alternative.

gjlipman · December 23rd, 2007, 1:03 pm

gjlipman · December 23rd, 2007, 1:03 pm

nparaschos · December 24th, 2007, 9:04 pm

I remember that article by Blanco. As the first PC explained more than 90% of the movement of the futures gas curve (at least for the NYMEX contract), I am still trying to determine the importance of calculating PCs for each individual monthly buckets. It may, however, be a good alternative for electricity futures where more than the first 3 PCs are needed to adequately model the whole forward curve. I would probably need to investigate this a bit further.