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

[Michael (D. portal) <mi...@da...>]

Hi Giuseppe:

Thanks a lot for your very insightful reply!

I will do B-S (Breeden-Litzenberger) implied probabilities first to see if
the results make sense before going to more sophisticated modelling.

This is great, thank you!

Michael

On Tue, Aug 31, 2021, 3:27 AM Giuseppe Trapani <tr...@gm...> wrote:

> 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
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>>>>>
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>>>
>
> --
>
> *Giuseppe Trapani*
>