Re: [Quantlib-users] Is Implied volatility method available for Asian option class

[Matthew K. <mat...@gm...>]

This is an interesting question and thank you for bringing it up. One
reason I think an impliedVolatility function is omitted from AsianOption
instruments is that there isn't a canonical definition for what implied
volatility means to an Asian option. Sure, there's always a definition of
IV for Black-Scholes type models where you can solve for the volatility
parameter, but if you notice in the VanillaOption class, impliedVolatility
is hard coded as the solution to an AnalyticEuropeanEngine if the
instrument has European exercise and FdBlackScholesVanillaEngine otherwise.
QL actually ties the definition of IV to an instrument, giving no used
control over what engine generates it. So, I would vote we never add an
impliedVolatility function to Asian options, because there isn't a
broadly-accepted definition of what engine should be used to define IV for
Asian options.

That said, if you want to just have some code in your local repo that
replicates the VanillaOption behavior, add this to the
DiscreteAveragingAsianOption header class:

Volatility impliedVolatility(Real price,
                                     const
ext::shared_ptr<GeneralizedBlackScholesProcess>& process,
                                     Real accuracy = 1.0e-4,
                                     Size maxEvaluations = 100,
                                     Volatility minVol = 1.0e-7,
                                     Volatility maxVol = 4.0) const;

And add this to the DiscreteAveragingAsianOption cpp file:

    Volatility DiscreteAveragingAsianOption::impliedVolatility(
        Real targetValue,
        const ext::shared_ptr<GeneralizedBlackScholesProcess>& process,
        Real accuracy,
        Size maxEvaluations,
        Volatility minVol,
        Volatility maxVol) const
                                     {
        QL_REQUIRE(!isExpired(), "option expired");

        ext::shared_ptr<SimpleQuote> volQuote(new SimpleQuote);

        ext::shared_ptr<GeneralizedBlackScholesProcess> newProcess =
            detail::ImpliedVolatilityHelper::clone(process, volQuote);

        std::unique_ptr<PricingEngine> engine;
        engine.reset(new
AnalyticDiscreteGeometricAveragePriceAsianEngine(newProcess));

        return detail::ImpliedVolatilityHelper::calculate(*this, *engine,
*volQuote, targetValue,
                                                          accuracy,
maxEvaluations, minVol, maxVol);
    }

You'll need to resolve some new dependencies in those files and recompile,
but that's it. Also note that I defaulted to using the
AnalyticDiscreteGeometricAveragePriceAsianEngine engine, but you can use
whatever you want there.

On Tue, Dec 7, 2021 at 6:03 AM Ashish Bansal <ash...@gm...>
wrote:

> Hi,
>
> I am trying to evaluate the Arithmetic averaging Asian option using QL
> class called DiscreteAveragingAsianOption. However, there is no method
> under it to calculate the implied volatility, which is present for plain
> vanilla and barrier options.
>
> Please help how can I calculate IV for Asian options.
>
> Regards,
> Ashish
> _______________________________________________
> QuantLib-users mailing list
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>


-- 
Matthew P. Kolbe
(312) 218-6595
mat...@gm...