Anyone can give me some ideas about how to define and calculate carry and roll-down return for swaptions? I am doing return attribution for a swaption portfolio. I am trying to use 0.5*convexity*vol^2*DeltaT to approximate the theta return. I doubt this approximation actually includes carry and roll-down. I am wondering if there is any way carry and roll-down could be defined and calculated directly for interest rate options.Thanks

Unfortunately nobody can compute the roll and carry of a swaption apart from Morgan Stanley, because in their infinite widsom, they patented the formula: patent number 7958036, Filing date Apr 9th 2009System and method for calculating a volatility carry metricThe same authors wrote this note that I found very well written and interesting; even if probably they don't expect it to be used since protected by the patent above:Long vol: The new carry tradeOh well... provided you don't write a computer system that takes input from a database or other source, performs some computations and returns the results to screen or other source you should be ok... (this is what the patent amounts to... in practise nobody can write a program ever again without having to pay money to Morgan Stanley)

Thanks, interesting article. However, my question is probably even more basic than Vol carry and roll down. I am wondering if I should expect any rate carry and roll-down for a instrument with optionality. The answer might be "yes". Then how should I calculate rates carry and roll-down for a swaption? same as a swap?

It'is true. I remember getting quite excited about this paper. I had no idea this had been patented though. In USD rates I never found such analyses of any use though, at least not on the buy side. Might be better in FX or equity space...

QuoteI am wondering if I should expect any rate carry and roll-down for a instrument with optionality. The answer might be "yes". Then how should I calculate rates carry and roll-down for a swaption? same as a swap?Yes you would: the fact that you are moving in time still means that (with the very strong and questionable hypothesis of same yield curve and vol surface) your rate has increased or decreased and therefore your option is now more or less in the money and therefore gained or lost value (so there is a roll on the vol surface as result of the roll on the rate). This is not a great secret but many shops break the calculation in different ways so there is not always a complete agreement on how best to attribute the effect of roll due to curve and vol roll.

That's what I thought. Then what about rates carry? I don't think I should expect any carry for a instrument with optionality or forward starting since simply there is no accrual. Is that right?

What are the transfer pricing policies of the firm? When you sell/buy a swaption you generate/consume funds. Funds generated/consumed by a trader usually enter/leave a centralized funding pool and have a rate charge credited/debited associated with them. This is often an overnight rate for a trading position since the length of a holding horizon in unknown.

yes, you can simply compute roll-down along all term structures, i.e. the rate curve (you can as usual separate the effect on the annuity and the forward), as well as ATM volatility curveand also along your stoch vol parameter curves. there is indeed a rate roll-down effect for options. that effect should be baked into the skew - obviously. moreover as for rates the forward looking roll down is a screwy measure as it need not realize at all. I mean do rates roll to spot? sometimes they do. sometimes they don't and the curve just reprices, i.e. it moves.I think that the carry concept introduced in the MS paper is more problematic since it relies strongly on delta hedging and that is screwy. I mean delta heding is good clearly, but thereis a model assumption in there. like what model do you hedge against? a BM, a GBM, a stoch vol model? these are all bad models.

Hi DFT,I am new member to this forum. I am working on the same issue as you were in Mar 2013 (creating a attribution frame work). I wanted to know if you found an answer to calculate the roll down and carry for the swaption. I understand that the swaption is an option. The option value will be sum of option value and intrinsic value. The intrinsic value will have rolldown and carry. I believe the roll down and carry of the time value part is theta (I could be wrong though). I would highly appreciate your inputs on this since you have probably already researched and found an answer to this.ThanksTapas