Problem with impliedVolatility using DividendEngine

[Ferghil O'Rourke]

Hi,

I’m new to QuantLib and am having a problem generating an implied volatility

for an Option when dividends are involved using DividendVanillaOption and

FDDividendAmericanEngine. If there are no dividends on the underlier I have

no problem generating a volatility using VanillaOption and FDAmericanEngine.

The following code gives a “not enough points to interpolate” error:

 

DividendVanillaOption option(stochasticProcess, payoff,

amExercise, dividendDates, dividendPayments);

 

Size timeSteps = 101; 

 

// Finite differences engine

option.setPricingEngine(boost::shared_ptr<PricingEngine>(

              new FDDividendAmericanEngine(timeSteps,timeSteps)));

       

// Sample volatility given this FDDividendAmericanEngine..

Volatility v = option.impliedVolatility(optionPrice, 1.0e-4, 20, QL_MIN_VOLATILITY,

                                                              QL_MAX_VOLATILITY);

 

Being a newbie, I lifted this pretty much from the AmericanOption sample but changed

to use the dividend classes. I populate dividendDates and dividendPayments with Dates

and Amounts for each dividend payment. I’ve also tried changing the timeSteps

parameter to be odd/even and no change – I always get the “not enough points to

interpolate” error.

 

Like I say, code similar to above using VanillaOption and FDAmericanEngine gives

me a reasonable looking volatility figure. Am I going about generating implied

volatility in the right way? Any help pointers greatly appreciated.

 

Thanks,

Ferghil O’Rourke

 

[Joseph Wang-2]

I'll try to take a look at this this weekend.  My guess is that the dividend
engine does a lot of shift of the grid so the pricing might be off the grid
that the dividend engine is expecting.

In the mean time can you try the following

1) Run the experiment with AnalyticEuropeanDividendEngine

if it fails - that probably means that the problem is the in the input
parameters

if it works then

2) Run the experiment with the FdEuropeanDividendEngine

Something else you can do is to vary the size of the dividend (i.e. set the
dividend at zero and see if it works, then increase till it fails)

One thing that you should be aware of is that the FD dividend engine in 0.3.11
does discounting in a way that results in different answers from the analytic
european engine and most classic treatments (i.e. Hull).  0.3.12 will have
two different dividend engines.

[Ferghil O'Rourke]

Hi, thanks for the reply.
I tried passing 0.0 as the dividend payment but even then I still get
the interpolate error. Might this indicate that the problem is with the
other parameters? That would seem strange as all the other params
except the Date vector work fine with the regular engine. The date
vector is just a regular vector of quantlib Date objects.

Also, in the Quantlib version I have there is no
AnalyticEuropeanDividendEngine or FdEuropeanDividendEngine. How do
I get those? The second one I will need actually, as my client wants
to be able to price European options using Black Scholes but
incorporating dividends.

Again, thanks for the help.


-----Original Message-----
From: [hidden email]
[mailto:[hidden email]] On Behalf Of Joseph Wang
Sent: Wednesday, February 15, 2006 12:40 AM
To: [hidden email]
Cc: [hidden email]
Subject: [Quantlib-users] Re: Problem with impliedVolatility using
DividendEngine

I'll try to take a look at this this weekend.  My guess is that the dividend

engine does a lot of shift of the grid so the pricing might be off the grid
that the dividend engine is expecting.

In the mean time can you try the following

1) Run the experiment with AnalyticEuropeanDividendEngine

if it fails - that probably means that the problem is the in the input
parameters

if it works then

2) Run the experiment with the FdEuropeanDividendEngine

Something else you can do is to vary the size of the dividend (i.e. set the
dividend at zero and see if it works, then increase till it fails)

One thing that you should be aware of is that the FD dividend engine in
0.3.11
does discounting in a way that results in different answers from the
analytic
european engine and most classic treatments (i.e. Hull).  0.3.12 will have
two different dividend engines.



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[Joseph Wang-2]

FYI, I just ran it against the version in CVS and it ran fine.  There were a
huge numbers of changes in the dividend engines recently so it may be that
there was a bug that has been fixed.  Luigi has already branched out 0.3.12
and it should be released shortly.  If you have a version older than 0.3.11
or want to test out CVS, you might try to see if this fixes things.

One other thing that would be useful is to set a break point where that error
happens and then e-mail me a stack trace.  

Something else to try is to calculate the NPV for the option and see if that
gives out any values.

The number that goes into the the constructor are actual amounts.  As far as
discounting, the 0.3.11 engine does not do discounting which gives answers
which are at variance with the standard reference texts.  The version in CVS
has two different engines that do discounting differently, and the default
does match the classic answers in Hull.

One other thing is that the answers may be (or may not be) wrong for American
options.  The trouble is that the engine shifts the price of the option only
when there is a dividend payout, and doesn't take into account the change in
the discount factor in between time steps.  This doesn't matter for European
options, but it might (or might not) matter for American options as it may
interact incorrectly with the step condition.  In any case, it would be a
very good idea to throw the engine against known good values before putting
any money on the answers.

At Thursday 16 February 2006 12:56，forourke wrote：
> Hey Joseph,
> For the dividend payment vector that's passed into the
> DividendVanillaOption() ctor, should those dividends be expressed
> as actual $amounts or are they as a % of the underlying price?
> Also, will the engine discount for present value of each amount
> or should I do that before putting them into the vector?