In my experience, the prices of American and European vanilla options are usually close to each other. I don't recall ever seeing more than a few percent difference, but anyway ... I'm working on a deal which, essentially, involves American-style spread option. Unfortunately, I don't have any model for this. Perhaps it's time to build a Monte-Carlo engine after alll ... Meanwhile:Could anybody point to an appropriate model? Could anybody state from the experience to the effect of (dis)similarity of American vs European-style spread options prices? Is there an intuitive argument as to why these should (not) be close, like vanillas?Many thanks,

What about a two asset binomial tree, if you are lazy and don't want to code it up yourself then buy my book where there is ready to use spreadsheets and VBA code for European and American spread option, but only with constant vol and correlation, geometric brownian motion.Monte Carlo is a good alternative for more complex stochastic processes.

The difference between American and European option prices depends mainly on the difference between the payout of the underlying and cash (or whatever is exchanged for the underlying) and the underlying volatility. The first increases linearly with time, the second with the square root of time. You will get the greatest relative difference for long-term options and options with low volatility relative to the difference in payout rates. One reason you don't see larger differences is when the differences become large people tend to structure the option to avoid them (such as adding payout protection, or structuring as a swaption). Most buyers are unwilling to pay a lot for American exercise, because they don't want to worry about optimal exercise. On the other hand, they like the flexibility of exercising when they choose, for convenience rather than economic advantage. Therefore, most sellers prefer to structure things so they don't need a big American surcharge.One reason the European/American difference is more important for spread options is you have two assets that can have large or uncertain payouts instead of one. For example, suppose I have a NYMEX Gasoline/Heating Oil Crack Spread Call. I'm $0.50 in the money based on spot prices in August, two months before my October expiry. But I'm $0.50 out of the money based on two-month forward prices. This spot/futures difference reflects an implied payout. Seasonal factors are very important for short-term options, market fundamentals can drive large differences in long-term options.You need a good model of your underlyings to get spread option prices. Using the spread volatility will sometimes give reasonable answers, but seldom good enough for pricing. You will almost certainly need a Monte Carlo pricing.

Thanks, Collector!I have your book. I just didn't realize that you had American spread implemented. The American and European option prices are nearly the same, as they are for vanillas, except for long maturities and high interest rates.If you got a problem with that, talk to Collector.

>The American and European option prices are nearly the same, as they are for vanillas, except for long maturities and high interest >rates.Dividend can have huge effect for spread options. For example deep-in-the-money call max(S1-S2-X,0) when asset 1 pays huge dividend (for example 20% annual dividend yield). In that case American spread option have huge value over European. But fat spreads is not everything, don't forget the nice European style!

Jon,I was indeed pricing options on futures. As you might be aware the interest rates are low now so the American and European prices came out close.E-mail me the Boyle's paper, please.Thanks!

Hi everybodyI've seen recently a paper of C.Alexander, where the authors prove that AMERICAN and EUROPEAN spread options on futures must have exactly the same price!http://papers.ssrn.com/sol3/papers.cfm? ... 012521This property is not obvious at all when using a trinomial approach for american spreads, but it's of course difficult to separate the "early exercise premium" from the numerical error involved. My results for American spreads on futures always tend to be a smidge above the European case.Any experience with that?

I checked up the paper lupascu provided, i.e. http://papers.ssrn.com/sol3/papers.cfm? ... id=1012521 .However I fail to see the conclusion at the bottom of p.15 from the equation (30), with $q*$ defined above eq.(29). If the conclusion is drawn from the premise, $q*=0$, I don't see why that would be true, when $q=0$. I obviously have missed something. Could someone please point it out? Thanks.

Hi KnightriderI had the same concerns when reading the proof in the paper. I've already contacted the authors and am awaiting their feedback.I'll let you know once I receive an answer.

Just a short update on that. The result stated in the paper seems to be incorrect in that form. One can easily construct a counterexample:Take a futures contract F1 on your favorite commodity and consider F2 a futures contract (same tenor as the first) on a synthetic commodity, whose price is always twice the first one. In this case F2 - F1 always equals F1, so the spread option is basically an option on a futures contract on the first commodity. The statement in the paper would in particular imply that an american and a european option on F1 must be equally priced. On the other hand, it's known that this is not the case, due to the early exercise premium.

I agree with lupascu.Besides, the present value of the payoff of the spread option on futures is $d(T)(\omega(F2-F1-K))_+$, where $d(T)$ is the discount factor, and $\omega=1,-1$ depending on whether the option is a call or a put. There is no way to get rid of the interest rate, and when the interest rate is very high, it does pay to exercise early even for a call. If the option is traded in futures style, i.e., marked to market continuously, the interest rate does not come into the picture, then by the convexity of the payoff, early exercise is never optimal for either a call or a put.