Re: [Quantlib-users] Option-market-implied probabilities for interest rate moves

[Giuseppe T. <tr...@gm...>]

Hi Michael,

apologies but I'm not getting your point: the result is valid for whatever
underlying (be it interest rates / stocks / commodities) and so on, it only
relies on option prices. You can compute those option prices with a model
or you can get them from the market and THEN you obtain the risk-neutral
density for the underlying.

As for the SABR being "specific for rates" I think it's a slight
misconception: the SABR model describes the dynamics of the underlying
under the forward measure so you can use it with whatever underlying. It
became sort of "standard" in IR markets since it's a very simple way to
improve the computation of hedging ratios: when pricing vanilla derivatives
in the Black-76 (or Bachelier) framework you can use it to parametrize the
volatility curve and compute smile-coherent greeks. Such a framework is the
most intuitive since it allows you to price the most common and liquid
derivatives (Swaptions and Caps/Floors) without the need to model
dependencies between the knots of the yield curve.

If instead you are interested more specifically in the dynamics of the
ENTIRE yield curve, you have to rely on term-structure models (for example
short-rate models or maybe more involved quasi-gaussian models accounting
for the skew or more modern markov-functional models). You work in a
Monte-Carlo fashion like this:

1) calibrate the parameters of the model to some "information carrying
derivatives"
2) simulate the yield curve at the horizon you need
3) compute whatever you are interested in (for example the 10y swap fair
rate) on that curve
4) aggregate all the simulation results

Now as for 1) term-structure models are typically low-dimensional so you
cannot "calibrate" to all the IR market derivatives. A common choice is a
set of coterminal swaptions or ATM caps/floors spanning the analysis
horizon.  Also depending on the model, 2) and 3) can have some analytic
formulas / approximations so maybe you can spare yourself the whole
simulation and compute directly what you need.




Il giorno mar 31 ago 2021 alle ore 03:18 Michael (DataDriven portal) <
mi...@da...> ha scritto:

> Thanks a lot!
>
> I see links like below Breeden-Litzenberger
>
>
> https://quant.stackexchange.com/questions/29524/breeden-litzenberger-formula-for-risk-neutral-densities
>
> This is very useful for B-S distributional assumptions and will work well
> for stocks. I am not sure if it will produce good results for interest
> rates which have different distributions (e.g. rates now are so low that
> are less likely to decrease than increase). But I will definitely give it a
> try. Another way to do this is to use SABR volatility model (which is
> specific for rates) but I am not sure if a simple solution exists to derive
> probabilities there.
>
> Thanks,
>
> Michael
>
>
>
>
>
> On Mon, Aug 30, 2021 at 11:36 AM Giuseppe Trapani <tr...@gm...>
> wrote:
>
>> Hi Michael,
>>
>> to add on the previous answer, the derivative is taken with respect to
>> the strike price of the option.
>>
>> It's pretty easy to derive by yourself starting from the general payoff
>> of an option (yielding a "model free result") or from the Black-76 formula.
>>
>> For extra directions check online "Breeden-Litzenberger result".
>>
>> Giuseppe Trapani
>>
>> Il lun 30 ago 2021, 15:28 Michael (DataDriven portal) <
>> mi...@da...> ha scritto:
>>
>>> Yes. Thanks! If you could point me in the right direction on where I can
>>> get code for this that would be great.
>>>
>>> Thanks
>>>
>>> On Mon, Aug 30, 2021, 8:47 AM Gorazd Brumen <gor...@gm...>
>>> wrote:
>>>
>>>> There is a well known formula that relates call/put prices to implied
>>>> pricing probabilities, related to the second derivative of the
>>>> call/put prices. You might need an implied option value
>>>> parametrization for that.
>>>> Regards,
>>>> G
>>>>
>>>> On Sun, Aug 29, 2021 at 5:56 PM Michael (DataDriven portal)
>>>> <mi...@da...> wrote:
>>>> >
>>>> > Hi All,
>>>> >
>>>> > I am looking for an algo to calculate option-market-implied
>>>> probabilities of interest rates moves derived from the premiums of interest
>>>> rate swaptions.
>>>> >
>>>> > E.g. market-implied probabilities from the prices of swaptions on
>>>> 10-year-swap rates. What is the market-implied probability that 10Y swap
>>>> rate will increase 25, 50, 75 bps, etc?
>>>> >
>>>> > Thanks,
>>>> >
>>>> > Michael
>>>> >
>>>> > _______________________________________________
>>>> > QuantLib-users mailing list
>>>> > Qua...@li...
>>>> > https://lists.sourceforge.net/lists/listinfo/quantlib-users
>>>>
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>>

-- 
*Giuseppe Trapani*