Posted by
Luigi Ballabio-2 on
URL: http://quantlib.414.s1.nabble.com/Help-with-fdAmericanOption-tp2452p2455.html
At 01:27 PM 4/9/03 -0700, Wry Boy wrote:
>OK i dusted off my old copy of Hull (2nd ed) and
>poured over the chapter on finite differences. It
>seems to me that timeSteps should properly be a some
>sort of function of time remaining and gridpoints
>should be a function of expected volatility... For an
>option expiring in 1 year, sure, 365 for timesteps
>makes sense, but, for an option expiring in 2 months,
>does it make sense to cut up 60 days into 365 discrete
>time chunks?
And that is why it is a value you choose and pass to the pricer, rather
than a fixed one :)
>Following that line of reasoning through
>-- does it make sense to use days remaining as the
>timeSteps value and, if we do this, will the model
>converge properly to accurate prices as timesteps is
>reduced each day heading toward expiration?
>A similar argument for gridPoints. Don't you need to
>divide that axis up into chunks that approximate your
>volatility-based expectation of where the stock can
>move to in the time allotted? For example, if I
>expect no greater than a 10 point range on a stock
>over the next 2 months and I want to be able to price
>the american option in 0.25 (underlying) increments of
>that range, can I deduce that:
>
>gridPoints = 10 / 0.25 = 40,
>timeSteps = 60 (i.e. days remaining)
>
>Does this make any sense?
It does in general, although for my own peace of mind I would make a
few tries---for instance, I would look at the results for 40x60, 80x120,
and 160x240 and check if the calculated price varies too much for its
own good. Calculations are fast enough to allow you to do that.
Also, I think there are a few constraints in the implementation of the
pricer. For instance, there's no place where you can *directly* input
your intuition on the no-more-than-10-point range---if I remember
correctly, the pricer will create itself a grid extending about four times
sigma*sqrt(T) above and below the current log price, so you'll have to
express your feeling through the value of the volatility.
Bye,
Luigi