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fOptions American options Implied Volatility

4 messages · msalese, David Reiner, stefano iacus

Original
msalese
# 
Hi guys,
working with RMetrics/fOptions library I see there isn't a function to
compute iv on American Options so I've build this function to do the job:

library(fOptions)

impVolAmCall<-function(pmkPrice,Und,Strike,expTime,rInt,pb){
  auxAmCall<-function(pVol,pmkPrice,pUnd,pStrike,pexpTime,prInt){
    at<-CRRBinomialTreeOption(TypeFlag = "ca", S = pUnd, X=pStrike,Time
=pexpTime, r = prInt, b = pb, sigma = pVol, n = 15)
    return(pmkPrice-at at price)
  }
  
limpVol<-uniroot(f=auxAmCall,lower=0.05,upper=2,tol=0.001,pmkPrice=pmkPrice,pUnd=Und,pStrike=Strike,pexpTime=expTime,prInt=rInt)
  return(limpVol$root)
} 

After that I downloaded options price from Italian IDEM on G.MI (Generali
Assurance) and loaded all in the obsPrice3 data.frame:

str(obsPrice3)
'data.frame':	12 obs. of  6 variables:
 $ expDays : num  59 59 59 59 59 59 59 59 59 59 ...
 $ YExpDays: num  0.234 0.234 0.234 0.234 0.234 ...
 $ Bid     : num  2.219 1.726 1.249 0.845 0.544 ...
 $ Ask     : num  2.266 1.769 1.293 0.883 0.579 ...
 $ Strike  : num  13.5 14 14.5 15 15.5 16 16.5 17 17.5 18 ...
 $ MidPrice: num  2.242 1.747 1.271 0.864 0.561 ...


expDays YExpDays    Bid    Ask Strike MidPrice
1       59 0.234127 2.2190 2.2660   13.5  2.24250
2       59 0.234127 1.7255 1.7690   14.0  1.74725
3       59 0.234127 1.2490 1.2930   14.5  1.27100
4       59 0.234127 0.8450 0.8830   15.0  0.86400
5       59 0.234127 0.5445 0.5785   15.5  0.56150
6       59 0.234127 0.3325 0.3670   16.0  0.34975
7       59 0.234127 0.1895 0.2180   16.5  0.20375
8       59 0.234127 0.1010 0.1280   17.0  0.11450
9       59 0.234127 0.0485 0.0760   17.5  0.06225
10      59 0.234127 0.0115 0.0445   18.0  0.02800
11      59 0.234127 0.0005 0.0830   18.5  0.04175
12      59 0.234127 0.0005 0.0775   19.0  0.03900

Now I'd like to compute the iv for all the chain so I've used mapply:

mapply(FUN=impVolAmCall,obsPrice3$MidPrice,obsPrice3$Strike,Und=15.75,expTime=59/252,rInt=0.01,pb=0.01)
but R replay with:

Error in uniroot(f = auxAmCall, lower = 0.05, upper = 2, tol = 0.001,  : 
  f() values at end points not of opposite sign

The point is that for otm options I'm not able to find zero in auxAmCall
(auxiliary function) coded inside impVolAmCall function. 
I'm new to R so I think that something is wrong in my code, can someone help
me ? 

Thanks
Massimo
http://r.789695.n4.nabble.com/file/n3528629/obsPrice3.rda obsPrice3.rda 

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David Reiner
# 
Massimo,
This stock has dividends, so you might have to use a different valuation model for American valuation.
Some sort of discrete dividend model should work.
HTH,
-- David


-----Original Message-----
From: r-sig-finance-bounces at r-project.org [mailto:r-sig-finance-bounces at r-project.org] On Behalf Of msalese
Sent: Tuesday, May 17, 2011 4:37 AM
To: r-sig-finance at r-project.org
Subject: [SPAM] - [R-SIG-Finance] fOptions American options Implied Volatility - Email found in subject

Hi guys,
working with RMetrics/fOptions library I see there isn't a function to
compute iv on American Options so I've build this function to do the job:

library(fOptions)

impVolAmCall<-function(pmkPrice,Und,Strike,expTime,rInt,pb){
  auxAmCall<-function(pVol,pmkPrice,pUnd,pStrike,pexpTime,prInt){
    at<-CRRBinomialTreeOption(TypeFlag = "ca", S = pUnd, X=pStrike,Time
=pexpTime, r = prInt, b = pb, sigma = pVol, n = 15)
    return(pmkPrice-at at price)
  }

limpVol<-uniroot(f=auxAmCall,lower=0.05,upper=2,tol=0.001,pmkPrice=pmkPrice,pUnd=Und,pStrike=Strike,pexpTime=expTime,prInt=rInt)
  return(limpVol$root)
}

After that I downloaded options price from Italian IDEM on G.MI (Generali
Assurance) and loaded all in the obsPrice3 data.frame:

str(obsPrice3)
'data.frame':   12 obs. of  6 variables:
 $ expDays : num  59 59 59 59 59 59 59 59 59 59 ...
 $ YExpDays: num  0.234 0.234 0.234 0.234 0.234 ...
 $ Bid     : num  2.219 1.726 1.249 0.845 0.544 ...
 $ Ask     : num  2.266 1.769 1.293 0.883 0.579 ...
 $ Strike  : num  13.5 14 14.5 15 15.5 16 16.5 17 17.5 18 ...
 $ MidPrice: num  2.242 1.747 1.271 0.864 0.561 ...


expDays YExpDays    Bid    Ask Strike MidPrice
1       59 0.234127 2.2190 2.2660   13.5  2.24250
2       59 0.234127 1.7255 1.7690   14.0  1.74725
3       59 0.234127 1.2490 1.2930   14.5  1.27100
4       59 0.234127 0.8450 0.8830   15.0  0.86400
5       59 0.234127 0.5445 0.5785   15.5  0.56150
6       59 0.234127 0.3325 0.3670   16.0  0.34975
7       59 0.234127 0.1895 0.2180   16.5  0.20375
8       59 0.234127 0.1010 0.1280   17.0  0.11450
9       59 0.234127 0.0485 0.0760   17.5  0.06225
10      59 0.234127 0.0115 0.0445   18.0  0.02800
11      59 0.234127 0.0005 0.0830   18.5  0.04175
12      59 0.234127 0.0005 0.0775   19.0  0.03900

Now I'd like to compute the iv for all the chain so I've used mapply:

mapply(FUN=impVolAmCall,obsPrice3$MidPrice,obsPrice3$Strike,Und=15.75,expTime=59/252,rInt=0.01,pb=0.01)
but R replay with:

Error in uniroot(f = auxAmCall, lower = 0.05, upper = 2, tol = 0.001,  :
  f() values at end points not of opposite sign

The point is that for otm options I'm not able to find zero in auxAmCall
(auxiliary function) coded inside impVolAmCall function.
I'm new to R so I think that something is wrong in my code, can someone help
me ?

Thanks
Massimo
http://r.789695.n4.nabble.com/file/n3528629/obsPrice3.rda obsPrice3.rda

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msalese
# 
Thanks much David ,
the problem is that RMetrics/fOptions has only this valuation code:

RollGeskeWhaleyOption	         Roll, Geske and Whaley Approximation,
BAWAmericanApproxOption	 Barone-Adesi and Whaley Approximation,
BSAmericanApproxOption	        Bjerksund and Stensland Approximation.

Only the first one take care of dividends !

What I'm trying to do is to valuate the iv smile in the same way as Sheldon
Natenberg or Robert G. Tompkins does in their books, build an iv function
and use that to run a what-if scenario on my positions.
  
So I'll tray to use RollGeskeWhaleyOption approx in the same way as done for
CRRBinomialTreeOption.




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stefano iacus
#
On 17 May 2011, at 11:36, msalese wrote:

            

      
      
      
    

        
this means that f() never crosses zero, either always negative or always positive. This happens a bunch of times when you try to estimate IV from, say, a "wrong" model or if market prices are way too off the theoretical (up to the wrong model for these data) price.

no real clue, just some experience

stefano

            

      
      
      
    

        

      
      
    

        
-----------------------------------
Stefano M. Iacus
Department of Economics,
Business and Statistics
University of Milan
Via Conservatorio, 7
I-20123 Milan - Italy
Ph.: +39 02 50321 461
Fax: +39 02 50321 505
http://www.economia.unimi.it/iacus
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