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karfey
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Joined: October 3rd, 2012, 12:37 am

Pull to par effect in Black Formula

November 16th, 2016, 5:29 pm

Hi all,
if we price Bond option using Black-Scholes modelling bond spot, I understand there is a pull-to-par effect. The vol tends to 0 as bond reaches maturity.
I read that this issue is circumvented when Black formula is used instead, modelling Bond Forward. Doesn't the forward price also tend towards par, and vol collapses to 0 too?
 
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DavidJN
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Joined: July 14th, 2002, 3:00 am

Re: Pull to par effect in Black Formula

November 16th, 2016, 8:13 pm

Because of the pull to par effect you described, it is common to quote bond options using yield volatility (a relatively stable number that doesn't have the pull to par effect) and then convert the yield vol into an equivalent price vol using the bond's duration or PV01 (value of a basis point).
 
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karfey
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Joined: October 3rd, 2012, 12:37 am

Re: Pull to par effect in Black Formula

November 18th, 2016, 3:22 am

Thanks for your insights!
Sorry for not being specific earlier, I am referring to a specific discussion in Rebonato's book "Modern Pricing of IRD" :

The naive traders simply did not appreciate the subtle, but fundamental, difference between the Black and the Black and Scholes formulas and the volatilities used as input for both, and believed the pull-to-par phenomenon to be relevant to the Black formula as well. The sophisticated traders understood that the Black formula, with the appropriate inputs, is perfectly correct and justifiable, and that no pull-to-par effect applies to a forward bond price (which remains of the same residual maturity throughout its life).
(accessible here:http://press.princeton.edu/chapters/s7425.html )
 
 
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Finatos
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Joined: July 28th, 2012, 8:18 pm

Re: Pull to par effect in Black Formula

January 4th, 2017, 9:19 pm

It is okay to ignore this pull to par effect when you have a short option (<1y) written on a long term bond (around 10 year). For option on short term bond, neither BS or Black model can over come this effect. You will nee more sophisticated model e.g. Hull-White, BDT model