I implemented kirk's model to price a calendar spread but the answer is always 10-50 cents off compared to the real value.Any suggestion as to what is the best model for pricing a calendar spread on a commodity(Crude oil ??)Any readings or articles ?? I need to get it done soon........and how should I calibrate this model to the real prices?

How are you deciding which correlation to use? Normally if you are using Kirk, you have to pick the correlation strike-by-strike in order to match the price: it's an "implied correlation" rather like an "implied volatility"

I think this is a good reference-Reference paper 'Pricing and Hedging Spread Options' by Carmona and Durrelman , SIAM Review vol45, No 4I am not using implied correlations , but just found out that implied correlation is always less than the one I am using, difference mostly of the order 0.02~0.04 currenlty i am using a model to calculate implied correaltion , but will have to write one myself now!do you know of any helpful source for the same?I need to calibrate the model to NYMEX spread option Prices.will appreciate any inputs wrt this,thanks

You will find thata) There is a correlation skew, so the same correlation will fit at least most of the option prices very badlyb) Using Kirk and a single correlation (empirically estimated?) is not going to make you very much money in the long run: you'll end up writing lots of options and blowing up when there's a curve dislocation.If you are calculating correlations from some other clever model and your correlations are always higher than NYMEX's and if (maybe a big if) you believe your model, than doesn't that tell you that NYMEX options are too expensive? You should sell some. How are you computing your correlations? Are you calculating different correlations for different strikes? It is rather unclear where you are getting your correlations. And not quite clear what you are asking.I know of no public code implementation of Kirk implied correlations, but it's kind of trivial: just 1-dimensional Newton's method/line-search will do, since you have everything in closed form. Any of the "Numerical Recipes in X" books have decent implementations.

thanks crmorcom for your input,my basic question is to price calendar spread using a model which gives a value close to NYMEX and the kirk model is not doing that!!!! for my model I was calculating correlations empirically (may be thats one reason why it was not close)!! and to get implied correlation I used a model which i need to replicate now, its sort of dependable model and I think the implied correaltion that it is giving is correct. The implied correlation is always less than empirical correlation in this casebut the question remains...is kirks model the best one to price a calendar spread option on commodities?

I don't know what an FEA model is, but any decent model that you use for CSO pricing should produce lower correlations for most strikes. Possibly not for very high strikes, but for strikes close to zero, this should be the case.Using the Kirk model with empirical correlations is a terrible way to price crude CSOs. You get no correlation skew, and your empirical correlations will not price big moves well and will not even be particularly stable. The empirical correlations might give you a very rough idea, but are not much use for relative-value judgements.If you are using Kirk simply as a way to quote prices (like we use implied vols for vanilla options), then that's fine - in fact it's the market standard. Is that what you're doing?

yes I am not hedging , just trying to price the CSO,I did not pay attention to correlation skews related to CSO's , can you suggest a place where I can increase my knowledge about why correlation is so imp for CSO'sthankyou,

There is a book by Edeyland and Wolyniec which has some stuff, and another by Geman. Most of the published literature on commodity options and exotics is rather limited, since commodity markets are more peculiar that equities or rates/FX and usually less liquid, and data are harder to get, so that academics tend not to use them for modeling very much. Read also lots of papers by Schwarz - e.g. Schwartz & Smith, Miltersen & Schwartz, Nielsen & Schwartz.Read the Kirk paper (I think it's in a book, actually - Google Scholar will find it for you) to understand how the model's derived and what drives it: you can use it to model any spread options where the log asset-prices are jointly normally distributed subject to the models other approximations.The correlation skew comes from the fact that the log returns are not joint normally distributed (and the model's wrong from high strikes, anyway), just like single asset prices don't follow black-scholes exactly which gives you a skew/smile. The spread option price, in general, depends on the joint distribution of the asset prices at expiration - the Kirk model is a very special form.To model spread options well, then, you need to have a joint model of oil futures prices at different tenors. Good models are proprietary, and I cannot tell you any of mine, I'm afraid. People try all sorts of exotic things: AJD spot price models, HJM models of the forward curve - pretty well anything you can imagine (and some you shouldn't).

Well, we could at least reveal that most such joint models of futures prices are based on the celebrated Gabillon model And with regards to capturing correlation skew, there's always a copula..

Regardless of the model used, would you not require the forward volatility for the further dated contract? Anyone ever looked at what this does to the correlation skew?

QuoteOriginally posted by: crmorcomIf you are using Kirk simply as a way to quote prices (like we use implied vols for vanilla options), then that's fine - in fact it's the market standard.I am in the process of trying to do precisely this for the crude markets, which led me to find this thread (among others). Looking at the front 5 futures contracts (March through July 2013), the correlations are all very close to 1, which leads to difficulty with calibration, unless I alter the model inputs somewhat.Taking a specific example from yesterday, April and May futures settled at 96.33 and 96.75 respectively, and the -0.35 strike call and put settled at 0.08 and 0.15. From a simple strike rule, I use 0.20503 and 0.21748 for the vols and set correlation to 1. This yields a Kirk vol of approximately 1.324%. But this generates a call and put price of 0.154 and 0.224. In order to match the market, I would need to generate a Kirk vol of nearly half this (0.0079).The problem stems from the fact that the individual leg vols are too far apart, so they can't cancel enough to match the market, even when correlation is set to 1. So the way I see it, if I want to use Kirk purely for quoting purposes, I need to depart from the model by relaxing or changing the inputs in some way, e.g.:(1) Allow correlation to exceed 1.0 (1.00125 works)(2) Apply an arbitrary vol shift to lower the input vol (kirk vol = sqrt(v1^2 - 2*rho*v1*v2 + v2^2) - 0.00534)(3) Modify the Kirk vol formula so that rho==1 always leads to zero vol (kirk vol = sqrt(v1^2 - 2*rho*v1*v2 + v2^2) - Abs(v1-v2))I'm leaning toward the first approach, because it's the smallest departure from the model, but I'm wondering what (if any of these) would be most useful, purely for quoting purposes.