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frolloos


Total Posts: 104
Joined: Dec 2007
 
Posted: 2020-02-05 06:29
I want to price certain long-dated non-IR derivatives and therefore should include stochastic rate dynamics.

Would like to avoid using too complex IR dynamics as it is not my main exposure. So I was thinking of including a short rate model.

The short rate model should be kind of realistic, tractable, and hedgeable. Any suggestions on which I should use?

Would HW1F be sufficient?

One man's Theta is another man's Gamma - Me

nikol


Total Posts: 923
Joined: Jun 2005
 
Posted: 2020-02-05 08:45
If it is not your main risk why vanilla discount is not enough?

The answer is yes, HWF1 is enough. But then check contribution of IR by zeroing its risk. You must get just discounted price. Of course, I assume that you model OTHER factors.
If this contribution is large. Define threshold by taste or ask trading desk. Typically, >5% contribution is significant. If ir-risk contribution is below that, then plain discounting is enough and you do not need this complication. If it is even above 20-25% then you should start thinking about correlation between IR-factor and OTHER-factor.

Given current negative rates regime, IR is around zero, hence this is not your main risk. Currently.
Credit risk contribution is more interesting to look at. Either as spread or considering default (close-out) scenario. i.e. you come into (B)CVA, MVA theoretical domain.

frolloos


Total Posts: 104
Joined: Dec 2007
 
Posted: 2020-02-05 10:21
>If this contribution is large. Define threshold by taste or ask trading desk. Typically, >5% contribution is >significant. If ir-risk contribution is below that, then plain discounting is enough and you do not need this >complication. If it is even above 20-25% then you should start thinking about correlation between IR->factor and OTHER-factor.

Yes this makes a lot of sense. I haven't looked at the difference between vanilla discounting and HW1F so that's the first thing to do. Maturities are 5y+, some 10y stuff, so even though near zero rates at the moment I am not sure where things will be in a few years.

It's equity derivs I am looking at. Always find it difficult to say something about the correlation between short rate and equity. Maybe it's easier to say something about the correlation between term structure shape and equity, but then the model will be more complicated.

>Credit risk contribution is more interesting to look at. Either as spread or considering default (close-out) >scenario. i.e. you come into (B)CVA, MVA theoretical domain

Yikes. I tried not to see the elephant in the room - thanks for pointing it out :)

Thanks - this is helpful.


One man's Theta is another man's Gamma - Me

nikol


Total Posts: 923
Joined: Jun 2005
 
Posted: 2020-02-05 12:50
Short term model on long horizon? I thought so.

In principle it makes a lot of sense, but you have to account then economical aspects.
RN-measure of course helps to balance portfolio at the moment, but in the long run these two will contribute:
- economics (If economy booms, then your IR will grow, if not - IR keeps negative. think of it as behavioral model for Wholesale and Mortgage clients) and
- capital cost (sort of term-structure within KVA calculation)

chiral3
Founding Member

Total Posts: 5127
Joined: Mar 2004
 
Posted: 2020-02-05 13:59
I think it depends on the derivative. In theory and in many applications E[exp(-rt).X(S)], r stochastic, equals exp(-rt).E[X(S)], r deterministic. If T is so far out that you are maybe using historicals, than the contribution from r could be stripped via a HW and sig^2 added to your vol. If the derivative is more complex, contingent claim X(S,r), I can’t make that first statement.

Also, when rates are really low, no arbitrage implies a large percentage of negative rates in HW. If you have some complex X(S,r) you may care about that.

Nonius is Satoshi Nakamoto. 物の哀れ

frolloos


Total Posts: 104
Joined: Dec 2007
 
Posted: 2020-02-05 14:53
@nikol:

> economics (If economy booms, then your IR will grow, if not - IR keeps negative. think of it as behavioral model for Wholesale and Mortgage clients) and

agree, but I am not sure how to model this properly without some sort of regime change model. I think when economy booms there is some positive IR/equity correlation, and then there is a phase where the two decorrelate or even negative correlation, and then markets tank and both equity and rates head south. So I guess on average a mildly positive correlation.. ?

@chiral3:

>Also, when rates are really low, no arbitrage implies a large percentage of negative rates in HW. If you >have some complex X(S,r) you may care about that.

Yes, good point and I have thought about this too. I have considered / am considering modelling the short rate as a displaced diffusion with a drift, and the displacement will of course bound the rates from below. I think this can strike a good balance between tractability and realism, e.g. I don't want a rate of -5% or less. Would you agree?

The derivatives I am looking at are of the form E[exp(-rt).X(S)], so what you wrote is fine. I may want to look at quanto-ed and compo-ed long dated equity derivs at some point which brings a whole new set of complexities with them, but not at this point.

One man's Theta is another man's Gamma - Me

nikol


Total Posts: 923
Joined: Jun 2005
 
Posted: 2020-02-06 22:44
I am wondering why these guys made simulation upto 2% precision. Maybe you can read and explain?

https://en.wikipedia.org/wiki/MONIAC

"To their surprise, Phillips and his associate Walter Newlyn found that MONIAC could be calibrated to an accuracy of 2%"


frolloos


Total Posts: 104
Joined: Dec 2007
 
Posted: 2020-02-07 11:57
Interesting device and idea. Reminds me a bit of getting macroscopic results from Thermodynamics (Moniac in this case) without having to simulate individual particles (Monte Carlo simulations).

No idea what they mean with the 2% and how it is calibrated.

One man's Theta is another man's Gamma - Me
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