Hi Is anyone familar with Spread Options, ie options on the spreads between two rates like the 10Y vs 30Y? Specifically how do we model them? I've heard that some people are modeling the spread while others are modeling the two rates individually and estimating correlations between the rates.Thanks-Raph

Can do it either way, may depend on what else you need to consider (like is the trade callable which may increase the factors for the call decision e.g. RMS rate as additional factor).If you want to model the spread then it is likely you need correlation anyway to derive the spread volatility as it is unlikely this is directly observable. You will also probably want to transform from lognormal process to normal process.

QuoteOriginally posted by: RaphHi Is anyone familar with Spread Options, ie options on the spreads between two rates like the 10Y vs 30Y? Specifically how do we model them? I've heard that some people are modeling the spread while others are modeling the two rates individually and estimating correlations between the rates.Thanks-RaphFrom a PDE point of view a spread option on two assets is a 2-factor PDE with a mixed derivative term (corresponding to correlation). There are closed-form solutions or even numerically.I think that modellling just the spread can lead to negative spread and hence BS is not applicable??

An idea could be to model the ratio 30Y/10Y and strike will be 1 ( If 10Y > 30Y the underlying will be less than one but still positive).germoz

If the forward spread itself is chosen as the state variable, one can further choose whether to model it as normal or lognormal. For yield curve options one would naturally want to assume the forward spread is normally distributed and for credit spread options a lognormal formulation makes more sense. There was a downloadable research paper on this available from the Chicago exchange a long way back, don't know if it is still available. Its simple enough stuff, but I surely have C source code available for this is you can't get details on the web.

Hmmm... the topic seemed rather familiar. Look in the "file share" section of this website and you can find a document I posted a year ago which includes the equations for the single-factor normal spread option model.

1. this is generally a one way market. there are only buyers of these options so there is significant skew no matter how you price it so generally these do not trade very often2. i price using the spread as the random variable. rationale being that 10/30s is liquid enough to observe a vol and you only need to estimate 1 parameter.3. while spread can be negative this shouldn't be an issue in euro (for a while anyway) so bs is usually more than adequate. thankfully, i don't trade sterling...

Thanks for the reply everyone, it really helped!! .... I think I'll use the spreads as the rv in modeling the spreadoptions!-Raph

...to re-enforce anfieldred's comment - do yourself a favor and never sell a yield curve spread option.... look at recent rate history.... 10y rates have traded in a 20bps range while short rate have jumped massively b/c of fed policy.... in the last year or so the 2/10 curve has been more volitile than the 10y outright... if given the choice of selling such and option or sticking a sharp pencil in your eye, i'd think about it carefully....