[R-SIG-Finance] RQuantLib: AmericanOptionImpliedVolatility bug

[Robert Harlow]

Doesn't the error message say root not bracketed? That is informative because it means there is no root, or no implied volatility, that gives you back your price of 14.5- this is what you should expect given your inputs.  In order for a volatility to exist an option must have a positive time value.

Bob

> On May 26, 2017, at 6:55 PM, Charles Duranceau <cduranceau at nial.ky> wrote:
> 
> Thank you Robert,
> I agree with you this is an extreme case and I don’t expect too much accuracy from the implied volatility I get, but my concern was more about the error message (a NA would have been more desirable)
> By changing the engine I managed a workaround but I thought RQL team (or someone else having the same problem) could be interested with that non-desirable behavior.
>  
> Regards
>  
>  
> From: Robert Harlow [mailto:rharlow86 at gmail.com] 
> Sent: Friday, May 26, 2017 3:32 PM
> To: Charles Duranceau
> Cc: r-sig-finance at r-project.org
> Subject: Re: [R-SIG-Finance] RQuantLib: AmericanOptionImpliedVolatility bug
>  
> Charles, my suggestion (which I doubt you will like) is to wrap your calls to implied volatility root finders (quant lib or any others) in a try block that returns NA on error.  Your example (very little or no time value) can be common if you are using mid prices from bid-ask quotes.  Note that when you plug the answer from your sum of squares root finding routine back into AmericanOption you get a value slightly above 14.5.
>  
> On Fri, May 26, 2017 at 11:46 AM, Charles Duranceau <cduranceau at nial.ky> wrote:
> Hi,
> 
> I found a problem with the function "AmericanOptionImpliedVolatility" in RQantLib which return an error for a specific set of conditions (but cannot identifies exactly what are these).
> I present a case related to a short term, very deep in-the-money put with negative interest rate that generate error message. I present a reproducible example below.
> I found the related function "AmericanOption" with default produce similar error when use in a routine to back-out the implied volatility.
> However, I found good result (no error)  when using the engine="CrankNicolson" :  a naïve routine for backing-out the implied vol with this function return a volatility.
> There's a work around but think this information may add more stability to RQL.
> 
> Best Regards
> Charles
> 
> 
> Case
> RQuantLib Version 4.2
> 
> R version 3.3.2 (64bits)
> 
> library(RQuantLib)
> 
> price = 14.5
> strike = 65
> Spot= 50.5
> Rate = -0.00361
> DividendYield = 0
> Volatility = 0.296
> YearToMaturity = 3/365
> 
> # error when Implied Vol
> AmericanOptionImpliedVolatility("put", price,Spot, strike, DividendYield, Rate,YearToMaturity, Volatility)
> 
> Error in americanOptionImpliedVolatilityEngine(type, value, underlying,  :
> 
> ../../../QuantLib-1.6.2/ql/math/solver1d.hpp:202: In function `QuantLib::Real QuantLib::Solver1D<Impl>::solve(const F&, QuantLib::Real, QuantLib::Real, QuantLib::Real, QuantLib::Real) const [with F = QuantLib::{anonymous}::PriceError; Impl = QuantLib::Brent; QuantLib::Real = double]':
> root not bracketed: f[1e-007,4] -> [1.955446e-003,3.006858e+000]
> 
> #also generate error
> AmericanOption("put", Spot, strike, DividendYield, Rate,YearToMaturity, Volatility)
> 
> # works well
> AmericanOption("put", Spot, strike, DividendYield, Rate,YearToMaturity, Volatility,timeSteps=150, gridPoints=149, engine="CrankNicolson")
> # backing out the implied vol naively works
> fImpliedVol(Volatility,price,"put", Spot, strike, DividendYield, Rate,YearToMaturity)
> 
> 
> fImpliedVol<-function(iniVol,Premium,Callput, Spot, Strike, DivYield, Rate,YrtoMat){
>   ftm<-function(ImpVol,Premium,Callput, Spot, Strike, DivYield, Rate,YrtoMat, iVol)
>   {
>     ov<-AmericanOption(type=Callput, underlying=Spot, strike=Strike,dividendYield=DivYield, riskFreeRate=Rate, maturity=YrtoMat,volatility=ImpVol,
>                        timeSteps=150, gridPoints=149, engine= "CrankNicolson")
>     er<-(Premium-ov$value)^2
>   }
>   imp<-optimize(f=ftm,c(lower = 0, upper = 1.5), tol = 1e-4,Premium,Callput,Spot, Strike, DivYield, Rate,YrtoMat)
>   return(imp$minimum)
> }
> 
> > sessionInfo()
> R version 3.3.2 (2016-10-31)
> Platform: x86_64-w64-mingw32/x64 (64-bit)
> Running under: Windows >= 8 x64 (build 9200)
> 
> locale:
> [1] LC_COLLATE=English_United States.1252  LC_CTYPE=English_United States.1252    LC_MONETARY=English_United States.1252
> [4] LC_NUMERIC=C                           LC_TIME=English_United States.1252
> 
> attached base packages:
> [1] stats     graphics  grDevices utils     datasets  methods   base
> 
> other attached packages:
> [1] RQuantLib_0.4.3 dplyr_0.5.0
> 
> loaded via a namespace (and not attached):
> [1] zoo_1.8-0        magrittr_1.5     R6_2.1.2         assertthat_0.2.0 DBI_0.6-1        tools_3.3.2      tibble_1.0       Rcpp_0.12.10
>  [9] grid_3.3.2       lattice_0.20-34
> 
> 
> >
> 
> 
> 
> 
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> 
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