Pricing a swaption

[d.koutsomito]

Hello there,

I am working on a project on pricing swaptions. I am currently trying to understand the theory which lies behind these options on swaps. However, I have a couple of questions so far:

1) In order to price a swaption, do we have to know the payments of the underlying swap?

2) Is it enough to know the value of both the floating and the fixed legs on the payment dates or should we also have to know the value of these between payment dates, i.e. on every day?

It would be very helpful if you provided me with some deeper insight on swaptions and about which are considered the most important points when one wants to price a swaption.

Thank you in advance.

 

[CasanovaJ]

1) In order to price a swaption, do we have to know the payments of the underlying swap?

It's not even possible to know (with any degree of certainty) what the payments are going to be for the floating leg... you can estimate them by looking at a forward curve, but that's it.

2) Is it enough to know the value of both the floating and the fixed legs on the payment dates or should we also have to know the value of these between payment dates, i.e. on every day?

A fancier variation of the latter, but it sounds like you still haven't completely learned yet what an option is-- try to start there first (and it would probably be easier to start with equity options).

 

[d.koutsomito]

It's not even possible to know (with any degree of certainty) what the payments are going to be for the floating leg... you can estimate them by looking at a forward curve, but that's it.

What I mean is that we have already simulated the floating rate using the stochastic model of our preference. I thought it was obvious. Therefore, we have estimated payments and gains of both positions of the swap.



A fancier variation of the latter, but it sounds like you still haven't completely learned yet what an option is-- try to start there first (and it would probably be easier to start with equity options).

My question here is that by knowing the value of the swap payer (or receiver) on the payment dates, e.g quarterly, is enough to price the value of the swaption, given the strike rate, or we have to know this value at the time points (days) between the payment dates as well.

 

[CasanovaJ]

If you were already able to "simulate the floating rate using the stochastic model of our preference," I'm a little surprised that for #2 you wouldn't already know how to apply the Black model... it seems like the problem is that you don't really understand what options are, cuz you claim to already know the necessary math...

 

[d.koutsomito]

If you were already able to "simulate the floating rate using the stochastic model of our preference," I'm a little surprised that for #2 you wouldn't already know how to apply the Black model... it seems like the problem is that you don't really understand what options are, cuz you claim to already know the necessary math...

To let you know that Black's formula is not the only way to price swaptions (when you know the law of the short-rate) that's why I don't care so much now about finding the 'fair price'. My major concern at this moment is to make it clear that I have understood the structure of swaps, thus of swaptions too. It seems that it does matter to know the price of the swap every day during the whole period in order to price the swap, but to price the swaption I guess that the payoff of the swaption on the payment dates would be enough but not sure about it. This is the point about which I am looking info. I would say that instead of keep insisting on saying that "you don't really understand what options are", you better provide me with info based on my questions; if you are able of doing so. Otherwise, it has no point for you answering the post.

 

[CasanovaJ]

OK, hold on... After a pretty vague question of "how do you price swaptions," I figured the goal here was to just help you understand/derive the Black model meaning that in response to questions of "1) do you need to know the underlying swap's cash flows, and 2) If so, at what frequency-- quarterly or daily," I've been trying to nudge you towards answers of "1) it's impossible to know them, and 2) you need to estimate them based on a continuous time distribution, not discrete..." You're saying now that you actually already understand Black, and that your real goal here is to come up with a model that's even fancier?

That's like beginning a thread with "how do you solve 2+2," and then revealing the next day that you're actually Bill Gates, and that what you're looking for is for someone to tell you how to compute it a microsecond faster than Titan... I apologize that we seem to have been on slightly different wavelengths here till now, but there's no need to get snippy here ... it's a friendly message board