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gileper
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Pricing inflation linked option

May 10th, 2006, 10:34 pm

I have to price the folowing bond that at every t pays Max(Min(y+0.6%,2.25*I(t-8,t-20)),0) where y is the 6m euribor and I(t-8,t-20) is the inflation rate between t-8 and t-20 months.How to price it? I started bootstrapping the inflation curve from zc infl. swap adding up the seasonality factors. Even at this stage I have founded several differences between the regression made by Lehman inflation paper and the other procedure tramo and x12.The payoff should be a sort of worst beetween 2 assets . But after how to procede? Bestgile
 
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JackInTheBox
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Pricing inflation linked option

May 20th, 2006, 11:50 pm

Do you think there really is correlation between1Y inflation return set 8 months ago ?
 
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gileper
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Pricing inflation linked option

May 21st, 2006, 4:52 pm

Yep...in this case I know, I can assume corr=0...so the only par. are the vols. I wonder If I can assume that inflation rate is positive so to use kirk's formula..Moreover the only guide I have is Lehman paper, Hughston and mercurio. Anybody has hot papers?thx very much, any comment is welcome!
Last edited by gileper on May 20th, 2006, 10:00 pm, edited 1 time in total.
 
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farmer
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Pricing inflation linked option

May 21st, 2006, 5:18 pm

QuoteOriginally posted by: gileperI wonder If I can assume that inflation rate is positiveEconomically, no. Even though Bernanke supposedly said he would throw bills out of airplanes. But if you can hedge against something that has the positive-only assumption priced in, then why not?
 
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figaro
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Pricing inflation linked option

May 21st, 2006, 6:16 pm

By inflation, do you mean the us cpi index or something like that? With vol around 1%, probability of it going negative in less than 10y is negligible.
 
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gileper
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Pricing inflation linked option

May 21st, 2006, 10:06 pm

yes an index. HICPXT (inflation EU excl. tobacco, bloomberg cptfemu). The maturity of the bond is 10 yr, ...Now I have any ideas about the level of the vol, but I did not imagine it was so low, at the order of 1-2 %.Given that the correlation is about zero and vol is low, the below payoff can be decomposed under the assumption of I>0 in a short call spread option and a long floating euribor so that I apply the Kirk approximation. The infl. vol is negligible wrt libor vol. so to have a raw price I could not take in cosideration vol of infl. for the moment.The inflation curve that I developed has the seasonality adj, but in my opinion is to verify if how sold us the bond has accounted the seasonality factors for building the forward inflation curve.Thxg.
 
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slym
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Pricing inflation linked option

May 22nd, 2006, 7:21 am

hi.hum. I'm afraid you also might have to deal w/ convexity adjustment ... I'm currently tackling the same sort of issue & it seems to be a real mess.good luckrgdsslym
 
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JackInTheBox
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Pricing inflation linked option

May 28th, 2006, 1:49 am

The vol is not lognormal vol -- 1% is 100bps (per year) & higher than most libors! Therefore 1-2% is not low at all.. In fact, I think it is too high & most of that has to do with option illiquidity. YoY inflation rates definitely can go negative -- Keep in mind that these are price inflations, which on a short-term basis have no causal relationships with monetary inflation.
 
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figaro
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Pricing inflation linked option

May 28th, 2006, 10:03 am

I quoted 1% lognormal historical mid. Who is selling it to you at 100bps normal?
 
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gileper
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Pricing inflation linked option

May 28th, 2006, 1:36 pm

Well, ok assuming that YoY can be negative, (even if on my forward inflaion curve this never happens, Jan(-8)/Jan(-20) and July(-8)/July(-20) ) I wonder if and how can calibrate vols.The only quoted options are GS with maturities may and june.Could you explaine me a step by step analisys, I am not so expert.Thx in adv
 
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figaro
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Pricing inflation linked option

May 29th, 2006, 6:17 am

Depends on whether you are buying or selling.
 
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gileper
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Pricing inflation linked option

May 29th, 2006, 2:31 pm

Seller ...then?? It is so different?Thanks!
 
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figaro
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Pricing inflation linked option

May 29th, 2006, 6:01 pm

Quote 3% indicative. It is different - if you were buying, it would be 50bps...Why do you insist on a semi-analytical formula - as a check, presumably?To elaborate on slym's point - at first order this is a put on libor struck at inflation forward + a fudge factor - because of convexity of the payout it isn't exactly the inflation forward.I would plot this payout as a function of the inflation strike and measure the convexity; then multiply that by inflation vol and you get the first order estimate of the adjustment.
 
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gileper
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Pricing inflation linked option

July 2nd, 2006, 9:22 pm

what do you mean with" would plot this payout as a function of the inflation strike and measure the convexity; then multiply that by inflation vol and you get the first order estimate of the adjustment"THere's a way of measure conv. plotting the payout?thnks
 
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verachi
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Pricing inflation linked option

September 7th, 2006, 2:15 pm

I dealt with this convexity bond:w*fix_rate+(1-w)*floatingwhere w is function of inflation. I solved isolating a term likefloating(t)*CPI(t)/CPI(0)=fwdEUR*fwdCPI*exp(volEUR*volCPI*correlationEURCPI)that is a quanto adjustment. You can calibrate volCPI and correlation let's say using for guide Mercurio papers. I have a doubt for correlation because my price is not exactly the same of my provider. And I cannot check the implied correlation in the market. What do u think?Fabio