[R-SIG-Finance] RQuantLib: AmericanOptionImpliedVolatility bug

[Robert Harlow]

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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