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BerndSchmitz
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(discount and forward) curve interpolation - sophisticated methods or keep it simple?

March 24th, 2017, 4:34 pm

Hi,

I would be interested in the interpolation methods predominantely used in the street. imO one should always keep it as simple as possible, i.e. use the most simplistic method that does not produce any undesired effects. Luckily live becomes much easier if you assume you have a library that clearly distinguishes between discount curves (e.g. FedFund) and forward curves (e.g. USDLIB3M):
- For forward curves I would always bootstrap and then work directly on forwardLiborRates (instead of pseudo discount factors) and interpolate linearly on these rates. For me there is no reason why to use a more sophisticated method (like spline interpolation) unless my traders tell me that it is not in line with what the market does
- For pure discounting curves I'm indifferent to using linear Interpolation on DFs, log DF or zeroRates. I do not care about how weird the forwardLiborRates would look on these curves as I simply never derive any forwardLiborRates from any such curve.
I'm still a bit uncertain about the FedFund case. This curves is in fact not a pure discounting curve but both a discount as well as a forward curve. However, I will never use it to calculate forwards from while not using it to discount these forwards at the same time (so the weird looking forwards will cancel out). So I think there shouldn't be any problem with using a simple interpolation method here either. 

I would be very intersted in your thoughts on that.

Thanks,
Bernd
 
frolloos
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Re: (discount and forward) curve interpolation - sophisticated methods or keep it simple?

March 24th, 2017, 4:44 pm

I am by no means an expert on discount curves. But above simplicity I would probably place minimal chance of introducing arbitrage (for any curve or surface/cube). I take it that goes without saying for you as well.
 
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outrun
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Re: (discount and forward) curve interpolation - sophisticated methods or keep it simple?

March 24th, 2017, 7:05 pm

Adding to froloos' remark about "minimal chance"..

A robust model-free method to evaluate how well your interpolation would perform relative to market prices is to do "leave one out cross validation". You pick all possible combinations N-1 quotes to fit your interpolation model, and then check how well it predicts the quote you left out.
 
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Paul
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Re: (discount and forward) curve interpolation - sophisticated methods or keep it simple?

March 24th, 2017, 9:20 pm

But above simplicity I would probably place minimal chance of introducing arbitrage (for any curve or surface/cube). I take it that goes without saying for you as well.
Some people just don't want to make money. What are you, some sort of commie prevert?!
 
frolloos
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Re: (discount and forward) curve interpolation - sophisticated methods or keep it simple?

March 25th, 2017, 6:26 am

Haha, yes a bit: I like games to start on a fair basis to minimize the chance of making money :-D

Image
 
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mtsm
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Re: (discount and forward) curve interpolation - sophisticated methods or keep it simple?

March 26th, 2017, 1:20 pm

Absence of arbitrage is actually overrated. You are better of with a simple flexible model with a little arbitrage, than with a overly restrictive arb free model. Noticed time and time again.

With regards to curves, it really depends on the end users. If you have a not overly sophisticated crowd at your end, what you say is probably OK. Admittedly ever since the ois-basis started being taken into account at depth, you can just interpolate forward rates on the forward curves, though nothing prevented you from doing that before or anything else for that matter. The only problem I am seeing with what you describe is that you might want to express n-1 of your curves as spreads to one base curve. I am a little rusty on this stuff, but in my understanding for risk management that's truly desirable. Otherwise it's just a bit more hacky, though manageable too I guess. Do you do that, if so how and which curve do you pick?

Other than that, I can see a lot of reasons why you would want to have better curves than what you describe. 
 
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BerndSchmitz
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Re: (discount and forward) curve interpolation - sophisticated methods or keep it simple?

March 27th, 2017, 7:00 am

Other than that, I can see a lot of reasons why you would want to have better curves than what you describe. 
Can you name any of those reasons?
The only problem I am seeing with what you describe is that you might want to express n-1 of your curves as spreads to one base curve.
Good point. I think in theory it doesn't really matter wether you express all curve delta individually or as one base curve per currency with the remaining curves being spread curves over that principle curve. In practice, as curves in one currency tend to strongly move together, I guess the second alternative saves you some hedging and bid-ask-spread.
If you have a not overly sophisticated crowd at your end, what you say is probably OK.
What would a (very) sophisticated crowd demand? For OIS curves obviously central bank meeting dates - but this works with a straightforward Interpolation method as well, doesn't it? Libor curves I may want to model as spread curves. I guess there is a lot more stuff I'm missing out here, which I'm very interested in :-)
 
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Gamal
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Re: (discount and forward) curve interpolation - sophisticated methods or keep it simple?

March 27th, 2017, 8:39 am

Absence of arbitrage is actually overrated.  
It's not. The worst thing that may happen to you is bleeding: regular small loss that you may not even spot. That often happens when your model isn't arbitrage free.
 
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Paul
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Re: (discount and forward) curve interpolation - sophisticated methods or keep it simple?

March 27th, 2017, 9:25 am

A. Or you might money. Shock, horror
B. You can lose money with arbitrage-free models
C. At least you will be alert to risk, rather than hiding it until it is too late!
 
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Gamal
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Re: (discount and forward) curve interpolation - sophisticated methods or keep it simple?

March 27th, 2017, 10:41 am

You can lose money with arbitrage-free models
Of course. There're two ways to loose money: blow-up or bleeding, bleeding is much more dangerous. The worst thing is to grow together with the market but  slower than your competitors because of bleeding. Usually you don't spot it, because you're happy to make money. That's happens quite often when your model is wrong.
 
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mtsm
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Re: (discount and forward) curve interpolation - sophisticated methods or keep it simple?

March 27th, 2017, 1:59 pm

You are just wrong about that Gamal. Absence of arbitrage is very much a theoretical concept. Most of the time you would not even be able to observe it. It's just not necessarily the way a real market works. Of course if you live in this silly quant world and you believe that rates and vols just exist and are tied together by some idealized contraints, I can't help. But that's not the way things work. Not my main point though. 

The problem is that most arbitrage free models are overly constrained (dynamically) and too complex. I am only saying that you can achieve something more practically useful if you neglect absence of arbitrage. Depends on your usage of course.
 
frolloos
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Re: (discount and forward) curve interpolation - sophisticated methods or keep it simple?

March 27th, 2017, 2:28 pm

Regarding whether no-arbitrage makes sense is really necessary or not, shouldn't there be a split between vanilla & exotic (I'd include a 20% strike vanilla put as exotic to be honest), buy side (mainly driven by views and usually not hedging the derivatives but buy and hold) & sell side (mainly market-making and hedging nowadays)? 
 
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Paul
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Re: (discount and forward) curve interpolation - sophisticated methods or keep it simple?

March 27th, 2017, 2:52 pm

No-arbitrage models are a way of inter/extrapolating to new places/products. They are indeed complex, perhaps just to confuse people. I've long thought that there might be ways of doing this that have no theoretical basis whatsoever but are simpler and just as "good."
 
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outrun
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Re: (discount and forward) curve interpolation - sophisticated methods or keep it simple?

March 27th, 2017, 4:49 pm

No-arbitrage models are a way of inter/extrapolating to new places/products. They are indeed complex, perhaps just to confuse people. I've long thought that there might be ways of doing this that have no theoretical basis whatsoever but are simpler and just as "good."
The more tradable product there are, the bigger and complexer the web of constraints between them. At some point the easiest way to find solutions is to try to find an underlying model that has enough degrees of freedom as well as extra constraints (like positive probabilities or some sort of smoothness, incrementally) to enforce realism. However, in general all these models forget about all sort of risk factors that make them fundamentally wrong. I'm still thinking that there might be ways to model the subjective nature of risks and rewards that underly "value". Without a good model of subjective values you can't model trading and price discovery.
 
frolloos
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Re: (discount and forward) curve interpolation - sophisticated methods or keep it simple?

March 27th, 2017, 5:35 pm

Agree with Outrun re the more tradable the product the more constraints there are. Someone want to trade an ATM option with me for an arbitrageable price (Paul? :))? Happy to do so but I will stick to the no arb price. Longer term variance swap - totally different game. Structured products rehedging, supply and demand, extocis premium etc come into play, not sure if you can actually model all these factors properly.

So imho, it really depends what you're looking at, but (disclaimer) I am relatively new to finance / trading and there are many with lots more experience in this forum.