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BigDaddy


Total Posts: 8
Joined: Mar 2015
 
Posted: 2015-03-31 05:38
Hello,

I am interested in pricing and hedging Bermudan swaptions , and so far I have implemented a pricer based on Hull-White model + PDE.
I chose this model because I needed something simple and easy to implement .The calibration is done on the coterminal swaptions quotes.

I would like to know how it is done in practice (on the street) : BGM? HJM ? Markov-functional?

Thanks.

mtsm


Total Posts: 195
Joined: Dec 2010
 
Posted: 2015-04-03 03:54
I don't think it matters that much to be honest given the state of the market. It's very shallow. I think it's crazy to see the amount of work that was done on the topic 10 to 15 years ago. Was it ever worth it? I was not around back then, but it just seems that a lot of it was about quants keeping themselves busy.

Whichever model you use: HW with skew (Cheyette), BGM or MF, the thing that counts is that you understand the premium discount mechanism of your model in relationship to the market clearing level and you're good to go. With that you can bid-ask in the broker market and also extrapolate client trades.

Normal HW is a little too simplistic though, maybe.

akimon


Total Posts: 566
Joined: Dec 2004
 
Posted: 2015-04-03 13:16
mtsm cannot be more spot on! I have traded bermudan swaptions for the past 10 years. Man ... I think I have been doing this forever. I'm glad it's not the only thing I'm doing.

To elaborate a bit, the more vanilla-like your model is (in terms of pricing the underlying european swaptions correctly), and the closer it can get to the market clearing level of berms via the discount mechanism (which can be outside-of-the-model), the less 'exotic' risk it will actually have, and hence you can just trade berms like europeans.

BigDaddy


Total Posts: 8
Joined: Mar 2015
 
Posted: 2015-04-05 05:42
Thank you for both messages.


Why the skew matters if we just focus on the underlying instruments? and why a simple Hull-white model is not sufficient ?
A HW model with piecewise constant volatilities should be able to price each underlying swaption.

How about hedging ?

Cheng


Total Posts: 2836
Joined: Feb 2005
 
Posted: 2015-04-05 12:36
A HW model with piecewise constant volatilities should be able to price each underlying swaption.

But how do you know which one to exercise, ie which one is optimal ?

"Sad wings of destiny / Where have they gone? / I know eternally / I'll carry on" (Rob Halford, Sad Wings)

BigDaddy


Total Posts: 8
Joined: Mar 2015
 
Posted: 2015-04-05 19:25
You dont know it, otherwise what will be the purpose of this product ?

I meant that we can calibrate each HW vol to each underlying swaption vol, and finally ,using a tree or a PDE , we can reprice these swaptions.

unsmt


Total Posts: 196
Joined: Jul 2014
 
Posted: 2015-04-05 20:35
It somewhat be confused connection between model pricing-calibration-pricing. Can you please specifies the necessity of calibration.

BigDaddy


Total Posts: 8
Joined: Mar 2015
 
Posted: 2015-04-06 03:16
A bermudan swaption is a model-dependent product, we need a model and the right parameters to price it.

unsmt


Total Posts: 196
Joined: Jul 2014
 
Posted: 2015-04-06 04:07
It seems that a bermudan swaption is a contract which is traded on the market which is defined regardless of the model. A pricing model of the sw-op represents an estimate of the fair price. It is well understandable. On the other hand it looks like that standard theoretical pricing models do not good enough and one needs to make changes in the original model to get better coincidence between theoretical model and historical pricing data. My confusion is that whether or not calibration contradicts the original model.

BigDaddy


Total Posts: 8
Joined: Mar 2015
 
Posted: 2015-04-06 05:13
not all Bermudans are standard and liquid.


unsmt


Total Posts: 196
Joined: Jul 2014
 
Posted: 2015-04-06 12:38

my question was about calibration. What is the reason of calibration?

unsmt


Total Posts: 196
Joined: Jul 2014
 
Posted: 2015-04-06 23:26
My question relates to the general idea of a pricing model calibration. Ca one specify what the essence of calibration regardless of a particular instrument. Thanks

BigDaddy


Total Posts: 8
Joined: Mar 2015
 
Posted: 2015-04-07 00:08
It is becoming off topic, but to answer your question. When you price a complex product, you look at the liquid instruments that are closely related to it . In our example, the underlyers of the bermudan swaptions (european swaptions). As I said before, a bermudan swaption is model-dependent, therefore we must choose an Interest-rate model to price it. Once we choose it, the minimum we expect from this model is to be able to reprice the underlyers, that is why we must calibrate the model .
Otherwise , I can choose any models and any parameters , and conclude that my Bermudan price is between -oo and +oo.

unsmt


Total Posts: 196
Joined: Jul 2014
 
Posted: 2015-04-07 12:55
Thanks BD for the answer. From your respond it is not clear the concrete sense of the statement" this model is to be able to reprice the underlyers, that is why we must calibrate the model". Is that means that we first define price of european swaption which can be exercise at a one fixed date at a future moment? If yes then Bermudian swaption is a version of American option on irs?

pj


Total Posts: 3331
Joined: Jun 2004
 
Posted: 2015-04-07 13:48
yes and Yes
wikipedia

OFFENDERS WILL BE TERMINATED

unsmt


Total Posts: 196
Joined: Jul 2014
 
Posted: 2015-04-07 17:14
In this case Whether the American option pricing is a calibration of the European one?Actually I am trying to understand how does calibration in derivatives pricing is defined? What kind of mathematics it is used?

BigDaddy


Total Posts: 8
Joined: Mar 2015
 
Posted: 2015-04-08 02:24
I dont want to be rude , can you post your questions outside this post, in another section?
I would be happy to answer them there.

To refocus on the matter, mtsm , you said something about HW being too simple, why is that so if I can replicate all underlying swaptions?

unsmt


Total Posts: 196
Joined: Jul 2014
 
Posted: 2015-04-08 04:31
We can simplify a swaption. Let S ( T , t , x ) be a stock price governed by GBM with known drift and diffusion coefficients defined for T > t and S ( t , t , x ) = x. The stock can be sell and buy at any time T > t and current price x reflects this opportunity. Assume now that stock can be sell or buy only at say two dates in future moments T1 < T2 . What will be the price of such bermudian type of stock? How it should be exercised? This stock much easier instrument than BerOpt.

unsmt


Total Posts: 196
Joined: Jul 2014
 
Posted: 2015-04-08 04:33
We can simplify a swaption. Let S ( T , t , x ) be a stock price governed by GBM with known drift and diffusion coefficients defined for T > t and S ( t , t , x ) = x. The stock can be sell and buy at any time T > t and current price x reflects this opportunity. Assume now that stock can be sell or buy only at say two dates in future moments T1 < T2 . What will be the price of such bermudian type of stock? How it should be exercised? This stock much easier instrument than BerOpt.

unsmt


Total Posts: 196
Joined: Jul 2014
 
Posted: 2015-04-08 04:34
We can simplify a swaption. Let S ( T , t , x ) be a stock price governed by GBM with known drift and diffusion coefficients defined for T > t and S ( t , t , x ) = x. The stock can be sell and buy at any time T > t and current price x reflects this opportunity. Assume now that stock can be sell or buy only at say two dates in future moments T1 < T2 . What will be the price of such bermudian type of stock? How it should be exercised? This stock much easier instrument than BerOpt.

silverside


Total Posts: 1411
Joined: Jun 2004
 
Posted: 2015-04-08 10:52
unsmt, a Bermudan on equity isn't really like a Bermudan swaption - it may be more useful to compare it versus an American on equity. For equity options there are tons of papers about early exercise.

unsmt


Total Posts: 196
Joined: Jul 2014
 
Posted: 2015-04-08 13:00
i see the difference between bermudan sw-op and equity. nevertheless there is a common possibility to exercise in particular dates. in my example stock price has a known distribution which simpler than spread C ( T ) = C ( T , t , c ) and K = 0. There is no transparent idea how to pick optimal time to exercise bermudian property in Black Scholes world. This obstacle should be a problem in pricing bermudan type of either equity or derivatives by using BS approach. In a similar obstacle in default problem on assumed Poisson time of default coming. This reduction of default time makes sense as approximation though it was not and probably difficult to verify this hypothesis. For bermudan instruments the assignment for the time to exercise given a stochastic underlying does not clear.

pj


Total Posts: 3331
Joined: Jun 2004
 
Posted: 2015-04-08 13:23
< Apologies to BigDaddy for spoiling the thread >

My answer is in the other thread

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kikiki


Total Posts: 2
Joined: Jun 2017
 
Posted: 2017-09-18 18:00
I recently got some Bermudan quotes and try to verify my implementation of models (HW, Shifted BK, BGM).

For example SBK, the model's calibrated to co-terminal europeans and I tried to find a mean reversion so the model is able to reprice the Bermudan. But the quote seems so low that mean reversion has to go to negative. For example, 30nc7 75/79 (Aug 2017). Even BGM needs an increasing forward volatility. Although co-terminal europeans are good, other part from the vol surface is far away the model price.

I am curious about "premium discount mechanism of your model in relationship to the market clearing level". Could anyone elaborate it more? The underlying swaps and europeans are discounted with OIS in my case. I don't know much details about these quotes (the quotes are from a friend's bloomberg). What kind of curves should we use to justify those bermudan quotes?

If discount (OIS) is correct, I think those Bermudans are so cheap compared to most expensive european. Which model is suitable to catch cheap berms? At least, negative mean reversion doesn't make any sense to me.

mtsm


Total Posts: 195
Joined: Dec 2010
 
Posted: 2017-09-19 02:59
You are completely off. Also, if you got quotes from some friend and just try to pipe it through a model, who cares frankly. Did you ever believe that any of these parametric term structure model are actually meaningful in the first place?

In the absence of adjustable parameters (which most of the time when adjusting is possible loose their meaning anyway), pricing/trading berms is a game of assessing the richness or cheapness to what you consider to be the natural cheapness level of your model. The model is used as a ruler only, price translation mechanism. The quoting convention in terms of a spread to underlying ATM swap rate is not a transparent measure of the value, it's just good for broker talk. It's more useful to translate the price discount you consider the right one as well as what you would consider being a rich or cheap level relative to that discount using a measure related to vol. Some people use mean-reversion spreads, others units of vega. In order to get a handle of the right price discount of your model (in other words, to calibrate your model ruler), you need to price traded berms on your model day in, day out.

I think you can almost completely forget about the economic significance of all these shitty, yet quite implementation-complex models. The discount mechanism is supply/demand driven for all I can think of.
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