A volatility bond pays the absolute difference between CMS rates observed at the begining and at the end of a (quarterly or yearly) period. In a variation of this product known as "volatilty bond with shout option", the holder of the bond can freeze the value of the CMS rate observed daily, i.e. exercise early. Does the shout option add or remove value?

It's hard to see how it could reduce the value (to the holder).

Yes this is true. On the other hand, if you think you've caught the highest or lowest CMS fixing, are you better off shouting it or gamma trading it? In the latter, you are left with the opportunity to gamma trade it again, whilst on the former you are not. If we agree it does not take value away, then does it add any ? Are you better off exercising the CMS spot, or gamma trade the CMS forward?

you guys are missing the point , from product trading experience (of vol bonds) I humbly add my 2 cents. The only way the Shout Option adds value in this product if the Payoff is capped at a certain point , for eg ABS CMS in Arr - CMS in adv capped at X% , once the cap is reached the client might want to shout the option lest the value drops again.from a risk management perspective there are other challenges, Feel free to PM me with your qs

furthermore , In the article by El Karoui, Jeanblanc-Picque and Shreve (1998) it is shown that a sufficient condition for reduction of an American option on a finite time horizon to a European option is that the pay-off function is convex and (0) = 0. This is a model-independent result and thus valid for all diffusion models. try and find the paper by Jonatan Eriksson named WHEN AMERICAN OPTIONS ARE EUROPEAN .....the real value of shout options will be clear

Indeed. There is slightly subtle point, though, and that is on what the underlying rate is. If by shouting you fix the index at the current rate out of spot, and by not shouting you will eventually fix at some future date's spot rate, your underlyings are two different rates, so there is some value to the shout option.

Can you provide some more explanation why the shout option does not have value? I can't really see it and the cited papers don't help much either.thanks

QuoteOriginally posted by: tulaCan you provide some more explanation why the shout option does not have value? I can't really see it and the cited papers don't help much either.thankssee section 20.2.2 of this

I have vol 1 which only says "it is intuitively clear that it is always optimal to postpone the shout" without going into details. I noticed it comes up again in Vol 3 but my copy has yet to arrive... Meanwhile, can you give some hint about the intuition? By the way, congratulations to your book, it is really impressive

Indeed a proof is given in volume 3. Intuitively, in the american option there is a balance of accelerating the payoff (and thus saving on time decay) versus giving up extra optionality. However, in the shout option, irrespective of the shout time, the payment occurs always at the end of the period -- so there is no extra value in accelerating the exercise. In particular, exercising earlier you give up on extra optionality of holding to the end but are not compensated for that by saving on time decay. Mathematically, it follows from the Jensen inequality. hope this makes sense

What do you shout on? Is it today's spot rate, or is it today's CMS adjusted forward rate (starting at the end of the period)? In the later case, how do investor and trading desk agree on the level?

spot CMS rate. so my argument is not strictly correct given the rate is different on different days. However the shout period is typically quite short and to a good approximation various drifts involved can be neglected, in my view

Thanks for your answer. I was thinking along these lines as well. However, what made me uncertain was the following: if you shout you get the PV of the inner value, which for a put can be strictly larger than the value of the (European) option. Since the vol bond is a straddle, there are regions where you would gain by shouting.What's wrong with this argument?

QuoteOriginally posted by: tulaThanks for your answer. I was thinking along these lines as well. However, what made me uncertain was the following: if you shout you get the PV of the inner value, which for a put can be strictly larger than the value of the (European) option. Since the vol bond is a straddle, there are regions where you would gain by shouting.What's wrong with this argument?for a put in the absence of discounting and dividends (the case we have here) the option value is always higher than the intrinsic (what I think you call inner) value

Intrinsic, sorry.If there is no discounting, then shout option = american option = european option, right? But why would that be the case here?