March 17th, 2008, 9:43 am
QuoteOriginally posted by: outrunQuote2.- Take the optimal position under the new forward curve and calculate the net profit, during the year, involving dynamic programming.Its complicated. Suppose you have a flat forward curve with the price of the last month a tiny bit higher than all other months. With dynamic programming & estimating the 'static intrinsic value', the optimal solution would be to fill it up in the initial months & sell the whole volume in the last most. Suppose that with that schedule a trader trades the forward markets & locks the intrinsic value.Now suppose that the different between the last months and all other increases..The trader won't be able to do a thing, because it has already hedged the intrinsic optimal schedule, making a tiny profit. The optimal intrinsic schedule doesn't change if the price difference increases, so the trader can't do a trade. He should have done stochastic optimization, looking at all possible future forwardcurves, and make a decision based on uncertain future curves instead of the intrinsic schedule.That is a good example. There are several approaches adopted for solving this type of problem, but my preferred method is stochastic DP. Whatever approach you choose, if it doesn't consider the stochastic nature at every decision point, then it will be missing something.What you gain with a rolling intrinsic valuation is certainty of profit at each point in time. What you lose, though, is possibility of greater profits, as demonstrated in the example provided by outrun. Remember that on the day, gas will be traded at spot, regardless of what forward deals you have in place. On the day, purchase from spot to meet your forward obligations. Also on the day, if the spot price is higher than your expected marginal value of gas in storage, sell some gas from storage. Transaction costs aside, these are two separate activities, which just happen to be in the same market.Put slightly differently, you can undertake a rolling intrinsic type of strategy without ever having any gas storage available to you. If you choose to use physical (or financial) storage to provide certainty in this strategy, that is fine, but it is not required, and you should realise that there is an opportunity cost for doing so. If you didn't use your storage space for hedging the rolling intrinsic deals, you would instead be able to use it for (hopefully) profitable trading against spot, hence the opportunity cost.