Posted by
Wry Boy on
URL: http://quantlib.414.s1.nabble.com/Help-with-fdAmericanOption-tp2452p2454.html
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? 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?
Phil
---
[hidden email] wrote:
>
> hi wryboy,
> I've tested that timeSteps=50 and gridPoints=50 are
> ok for american option.
> It corresponds to the discretization of the time and
> underlying value.
> You know when you represent a plan with x axis=time
> and y axis = underlying
> you can draw a grid if you divide x axis in 50
> equally spaced intervals and
> the same for y axis.
> In one word, the higher is this value and the more
> accurate is your
> pricing.
> So timeSteps=500 and gridPoints=500 should give a
> better pricing than
> timeSteps=50 and gridPoints=50 but it's so small
> than you are going to lose
> performance for no advantage in term of pricing.
>
> If you need to price thousands of options (I did the
> same but with milions
> of options) I would also recommand an analytical
> approximation like Barone
> Adesi Whaley if performance is critical to you.
> I did the developpement in my Quantlib 0.3.0 and can
> share the code with
> you if you can help me to check it and test if
> there's no bug.
>
> Xavier
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