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by yougy60
August 2nd, 2013, 7:33 am
Forum: Technical Forum
Topic: Floor strike 0%
Replies: 8
Views: 9611

Floor strike 0%

<t>My underlying is the LIBOR rate for USD, EUR and CHF.My first idea was to keep the same prices for k<alpha (shifted lognormal) and the same prices for k>beta (lognormal). And for k into [alpha, beta] to take some convex combination of the two pricers. One problem is that alpha and beta will be de...
by yougy60
August 1st, 2013, 12:35 pm
Forum: Technical Forum
Topic: Floor strike 0%
Replies: 8
Views: 9611

Floor strike 0%

<t>Hi,Thanks for replying. To be more precise on my requirements, I would like the prices (1) to be near the lognormal prices when strike is large AND (2) to be near the shifted-lognormal prices when strike is low.I think I stated all requirements now. Sorry for unclarity.So, Pimpel, your solution i...
by yougy60
July 31st, 2013, 6:44 am
Forum: Technical Forum
Topic: Floor strike 0%
Replies: 8
Views: 9611

Floor strike 0%

<t>Hi,Thanks for replying.You are right, I forgot that I would like the prices to be near the old prices (ie lognormal prices) when the strike is >0,5% (ideally equal to the lognormal prices from a certain strike).So that the users of the pricer do not note any change in the prices for large strikes...
by yougy60
July 30th, 2013, 1:38 pm
Forum: Technical Forum
Topic: Floor strike 0%
Replies: 8
Views: 9611

Floor strike 0%

<t>Hi,I have a lognormal floor pricer and a shifted-lognormal floor pricer.The lognormal pricer is bad for low strikes, because the prices of the floor converges to 0 when strikes goes to 0% (ie it neglects the possibility of negative interest rates).So that for the moment I use the lognormal pricer...
by yougy60
July 17th, 2013, 11:16 am
Forum: Technical Forum
Topic: Hull White 'theta' derivation/proof
Replies: 2
Views: 8242

Hull White 'theta' derivation/proof

Hi,If you speak french, you can read propostion 2.9 p.24http://fiquant.mas.ecp.fr/ioane_files/InterestRatesModels-LectureNotes2011.pdf
by yougy60
July 16th, 2013, 3:20 pm
Forum: Technical Forum
Topic: Libor 3M-6M volatility
Replies: 58
Views: 20856

Libor 3M-6M volatility

Personally, I use the methodology without basis when such a case happens (Displaced Diffusion vol cannot be converted to Black vol).It is pretty uncommon, but if anyone has any suggestion about this, you are welcome.
by yougy60
July 15th, 2013, 1:39 pm
Forum: Technical Forum
Topic: Libor 3M-6M volatility
Replies: 58
Views: 20856

Libor 3M-6M volatility

He says that we may interpret sigma as a displaced diffusion volatility sigmaDD, where sigma is dSt = sigma * (St + b) dWt and S the OIS (see p. 10.)So, eta is not the sigma in the SDE you typed whereas sigma is the sigma in the SDE you typed.
by yougy60
July 15th, 2013, 11:41 am
Forum: Technical Forum
Topic: Libor 3M-6M volatility
Replies: 58
Views: 20856

Libor 3M-6M volatility

No because in Joerg's paper it is :dSt = sigma * (St + b) dWt (where S is the OIS and b the libor-ois spread)
by yougy60
July 15th, 2013, 11:27 am
Forum: Technical Forum
Topic: Libor 3M-6M volatility
Replies: 58
Views: 20856

Libor 3M-6M volatility

Ok if I understand, you have divided both sides by beta.And then?
by yougy60
July 15th, 2013, 10:43 am
Forum: Technical Forum
Topic: Libor 3M-6M volatility
Replies: 58
Views: 20856

Libor 3M-6M volatility

<t>Hi wadwad.I am not sure to understand what you say.Let F be the OIS and b the libor-ois spread.By definition of beta, we have b=F0*((1-beta)/beta) , so that dFt = sigma*(Ft + F0*((1-beta)/beta)) dWtDo you agree with this?If yes, which formula do you use to convert sigma into a black volatility? <...
by yougy60
July 15th, 2013, 8:27 am
Forum: Technical Forum
Topic: Libor 3M-6M volatility
Replies: 58
Views: 20856

Libor 3M-6M volatility

<t>Hi Lapsilago,The formula you refer to (ie from Jaeckel quanto skew paper) is the formula for the following DD modelisation :dSt = ( S0*sigma*(1-beta) + sigma*beta*St ) dWtHowever, in our case, the DD modelisation is simply :dSt = sigma * (St + b) dWt (where S is the OIS and b the libor-ois spread...
by yougy60
July 11th, 2013, 2:51 pm
Forum: Technical Forum
Topic: Libor 3M-6M volatility
Replies: 58
Views: 20856

Libor 3M-6M volatility

<r>Hi,Thanks for replying.I found the article you refer to : <URL url="http://www.pjaeckel.webspace.virginmedia.com/QuantoSkew.pdfHowever"><LINK_TEXT text="http://www.pjaeckel.webspace.virginmedi ... pdfHowever">http://www.pjaeckel.webspace.virginmedia.com/QuantoSkew.pdfHowever</LINK_TEXT></URL>, I ...
by yougy60
July 10th, 2013, 1:07 pm
Forum: Technical Forum
Topic: Libor 3M-6M volatility
Replies: 58
Views: 20856

Libor 3M-6M volatility

<t>You can anyway find an inconsistency when you look at the call arbitrage boundaries :Let Y be the libor, X the OIS. Then you have dXt = sigmaBLACK * Xt * dWtdYt = sigmaDD * (Xt+basis)* dWtYou want to egalize Call(Xt,K=X0) and Call(Yt,K=X0+b)Call(Yt,K=X0+b)=Y0 (2*N(0.5*sigmaDD*sqrt(T))-1)The arbit...
by yougy60
July 10th, 2013, 12:49 pm
Forum: Technical Forum
Topic: Libor 3M-6M volatility
Replies: 58
Views: 20856

Libor 3M-6M volatility

Hi,Thanks for replying.Could you please tell me where you found your formulaes?The one I used is from equating the black call price with the shifted black call price with strike K+shift.I don't understand how a beta can occur in argument of N(). Thanks
by yougy60
July 10th, 2013, 7:03 am
Forum: Technical Forum
Topic: Libor 3M-6M volatility
Replies: 58
Views: 20856

Libor 3M-6M volatility

<t>Hi,As the approximation was not precise in this case, I already tried to use the analytical formula. However, it doesn't have a solution because the argument in N^{-1} (inverse cumulative normal distribution) is >1.The analitycal formula I used to convert Black vol into DD vol is :sigmaBLACK = (2...