Hi All,Working on valuing a situation where we literally store Oil in a VLCC, fully capturing the embedded optionality. Physical traders often store Oil in slightly backwardated markets, where there is no Futures spread that can be locked in by selling a physically settled later dated leg (short Oil Future). So the problem is, how do you price this today given the traders ability to dynamically hedge the cargo ie lock in some spread if the curve steepens OR sell on spot if the price rises. This is like asymmetric +ve Gamma - thoughts pls?I've simplified the problem as such (evaluating at any future month with Futures price Ft, we buy the spot via going long a Future today (Fo) ie RECEIVE physical oil at spot=Fo and storing it in a vessel. S= Spot at any time in the future). In practice it is the other way around (at inception they DONT hedge, but Ive priced it starting from the point of being fully hedged at inception)PnL = (Ft - Fo) + (S - S) #this is fully hedged as the physical legs offset eachother, we want to maximise this by un-hedging partially and selling part of the cargo on the Spot mkt if S>FtMax(PnL) = {aFt + (1-a)S} -Fo + (S - S) # a is some hedge ratio = a(Ft - S) + (S - Fo)So how do we optimise a? Well, if at time t S>Ft then we want to have a=0 ie fully sold on spot market or if S<Ft stayed at our hedge asPnL(optimal) = either (Ft -Fo) if Ft>S OR (S- Fo) elseHow do we price it today? I used a = 1- N(d1), which is the Delta of being short a (on S-Fo)This gives: V = (Ft - Fo) + N(d1){ S - Ft} = PnL(optimal as before) # this makes intuative sense because N(d1) is the % probablity of this S>F, in which case (like a CALL in this case) the S comes in and the Ft's are cancelled outSimply from recognising the explicit terms, this is the structure of:V= (Ft - Fo) + (long(Binary Asset or nothing, K=Ft) + short(Binary, Future or nothing, K=Ft)Makes perfect sense in practice because this embedded optionality is binary in nature and the Future would be perfectly offset and replaced with Spot).But this isn't path dependant? Well, pricing it like an American Binary (aka a One Touch Option) we incorporate path dependence, but then why would a trader completely unhedge the second S>K=Ft?Ultimately the value is if the trader sells fully unhedged and sells it on the spot market at Smax before maturity t. The pay off of a fixed strike look-back LCfixed = max{Smax - Ft, 0} with the strike K=Ft. Lookbacks are always ITM so also intuatively represent some value in the trade in backwardated market.We want (worst case locking in the spread): max{Ft, S} - FoSO:max{Ft, S} - Fo = LCfixed - Fo = max{Smax - Ft, 0} + {Ft - Fo} = EITHER (Ft - Fo) if S<Ft= OR (Ft - Ft) + Smax - Fo if S>FtMy trader thinks this is like asymmetric +ve Gamma - thoughts pls?Cheers

Thanks so much for the response. I have decided to utilise valuation of Passport options as at the heart of it lies a Hamilton-Jacobi-Bellman. A passport option would have a pay off of max(Balance, 0) where the Balance is the (Ft-S) whereby the holder can trade Spot at any time limited to a cash balance of Ft --- I explained that poorly but it is essentially a Call Option on any trading of a portfolio whereby you keep any gains but dont pay for any losses on any trading strategy which may or may not be perfect but may be what the trader thinks is optimal.This incorporates FW optionality (I think). As we are a producer we will always store the physical as opposed to using this as a trading strategy. What do you think?

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For valuation can't you chop it up into monthly CSOs? at least to a 1st approximation.Out of interest, what is the price of hold a VLCC for a month, and of pumping crude into and out of one as a %age of the underlying?QuoteOriginally posted by: ncutler1990Hi All,Working on valuing a situation where we literally store Oil in a VLCC, fully capturing the embedded optionality. Physical traders often store Oil in slightly backwardated markets, where there is no Futures spread that can be locked in by selling a physically settled later dated leg (short Oil Future). So the problem is, how do you price this today given the traders ability to dynamically hedge the cargo ie lock in some spread if the curve steepens OR sell on spot if the price rises. This is like asymmetric +ve Gamma - thoughts pls?I've simplified the problem as such (evaluating at any future month with Futures price Ft, we buy the spot via going long a Future today (Fo) ie RECEIVE physical oil at spot=Fo and storing it in a vessel. S= Spot at any time in the future). In practice it is the other way around (at inception they DONT hedge, but Ive priced it starting from the point of being fully hedged at inception)PnL = (Ft - Fo) + (S - S) #this is fully hedged as the physical legs offset eachother, we want to maximise this by un-hedging partially and selling part of the cargo on the Spot mkt if S>FtMax(PnL) = {aFt + (1-a)S} -Fo + (S - S) # a is some hedge ratio = a(Ft - S) + (S - Fo)So how do we optimise a? Well, if at time t S>Ft then we want to have a=0 ie fully sold on spot market or if S<Ft stayed at our hedge asPnL(optimal) = either (Ft -Fo) if Ft>S OR (S- Fo) elseHow do we price it today? I used a = 1- N(d1), which is the Delta of being short a (on S-Fo)This gives: V = (Ft - Fo) + N(d1){ S - Ft} = PnL(optimal as before) # this makes intuative sense because N(d1) is the % probablity of this S>F, in which case (like a CALL in this case) the S comes in and the Ft's are cancelled outSimply from recognising the explicit terms, this is the structure of:V= (Ft - Fo) + (long(Binary Asset or nothing, K=Ft) + short(Binary, Future or nothing, K=Ft)Makes perfect sense in practice because this embedded optionality is binary in nature and the Future would be perfectly offset and replaced with Spot).But this isn't path dependant? Well, pricing it like an American Binary (aka a One Touch Option) we incorporate path dependence, but then why would a trader completely unhedge the second S>K=Ft?Ultimately the value is if the trader sells fully unhedged and sells it on the spot market at Smax before maturity t. The pay off of a fixed strike look-back LCfixed = max{Smax - Ft, 0} with the strike K=Ft. Lookbacks are always ITM so also intuatively represent some value in the trade in backwardated market.We want (worst case locking in the spread): max{Ft, S} - FoSO:max{Ft, S} - Fo = LCfixed - Fo = max{Smax - Ft, 0} + {Ft - Fo} = EITHER (Ft - Fo) if S<Ft= OR (Ft - Ft) + Smax - Fo if S>FtMy trader thinks this is like asymmetric +ve Gamma - thoughts pls?Cheers

QuoteOriginally posted by: outrunThe U.S. Has Too Much Oil and Nowhere to Put It"Overflowing storage tanks could lead to another drop in prices"Zero Hedge was saying a similar thing earlier this week.Sell oil stocks, but baltic index.

QuoteOriginally posted by: rmaxQuoteOriginally posted by: outrunThe U.S. Has Too Much Oil and Nowhere to Put It"Overflowing storage tanks could lead to another drop in prices"Zero Hedge was saying a similar thing earlier this week.Sell oil stocks, but baltic index.Well, they could always load it on to a train and derail it someplace.

QuoteOriginally posted by: outrunQuoteOriginally posted by: Traden4AlphaQuoteOriginally posted by: rmaxQuoteOriginally posted by: outrunThe U.S. Has Too Much Oil and Nowhere to Put It"Overflowing storage tanks could lead to another drop in prices"Zero Hedge was saying a similar thing earlier this week.Sell oil stocks, but baltic index.Well, they could always load it on to a train and derail it someplace.I once made models for the all the power plants at Corus (large steel producer). Part of the model was the put option to flame away all the gas that got produced. It had quite a bit of value!Somebody about 10km from my house needs your model. About once every week or two, they flare off a huge amount of gas. The flame is on the order of 10-20 m high. I'm sure I could heat my whole house for a year on what they burn off in 15 minutes.

We're looking at about USc 5-8/Mt of Oil. Cant use CSOs, not sure why but old trader said model just doesnt work. The Lookbacks are good as they incorporate value of going fully hedged and locking in the spread at inception, selling on spot today, or waiting and selling tomorrow. HOWEVER, it doesnt capture the dynamics of the FW curve ie waiting and hedging with tomorrows spread. Requires Schwartz and Smith (2000) 2 factor stochastic FW curve model, quite a lot of literature on it. Then using that to optimise. Just a bit difficult to implement in excel....

In general I have a preference for factor models that directly model forward prices (HJM like), rather than models that model spot and convenience yield. I understand that specifying one implies the other, but using the former a) calibration is often easier; b) you don't have to explicitly deal with all kinds of convenience yields (which can be a mess and not smooth at all), c) implementation is often very easy and d) they align better with how I naturally think about forward curves.I like this master thesis a lot: http://dspace.mit.edu/bitstream/handle/ ... 383331.pdf . It doesn't have lookback valuation in it, but extending the results to do that (using MC) shouldn't be too hard I guess.