
First, you must try to get the same price, regardless of the valuation procedure. Indeed, for vanilla options, the binomial method, PDE, Monte carlo, and the BS formula all give the same result, provided you input the same parameters (interest rate being one of them). 

Second, the BS model is not simply discounting expected terminal payoffs. Discounting is done  in the risk-neutral measure, and several assumptions go into the derivation- one such is that instantaneous risk-free rate is assumed to be constant. The interest rate in the BS formula is the continuously compounded short rate, regardless of maturity. So if you want to incorporate term structure of interest rates , you may try  stochastic interest rate and numerically price.

Best wishes for the New Year,

Mahesh.

Sent via BlackBerry

-----Original Message-----
From: "Micha Keijzers" <micha.keijzers@gmail.com>

Date: Tue, 30 Dec 2008 09:55:06 
To: Mahesh Krishnan<heshriti@gmail.com>
Cc: bogaso christofer<bogaso.christofer@gmail.com>; <r-sig-finance@stat.math.ethz.ch>
Subject: Re: [R-SIG-Finance] Newbie question on risk free Interest Rate


I would say, the interest rate to choose depends on the valuation method. If
you would be using a tree method, using for example daily steps, use 1-day
(forward) rates in every step. In effect, this is then daily replication of
the payoff of the option. If you would be using Black-Scholes, take the
interest rate that matches the maturity of the option. The Black-Scholes
formula is simply the discounted payoff of the option.

Regards,
Micha

2008/12/30 Mahesh Krishnan <heshriti@gmail.com>

> Basically, if the instrument you are using is marked to market and hence,
> replicated continuously, you use the shortest possible interest rate. This
> is true for all futures and options, not forwards. For forwards and bonds,
> you match the tenor, aka maturity, of the instruments you are trying to
> price.
>
> As suggested by the other contributor, you may want to look at Libor rates
> as proxy for short rates. In any case, these rates don't matter much in in
> pricing options. Your vol. assumptions play a bigger role.
>
> Good luck,
>
> Mahesh.
>
> On Mon, Dec 29, 2008 at 1:32 PM, bogaso.christofer <
> bogaso.christofer@gmail.com> wrote:
>
> >  Thanks Mahesh,
> >
> >
> >
> > Yes it is now clear to me what interest rate should I take for Options.
> For
> > any option with different life time, Overnight interest rate, I have to
> > take. However if I take 3-month T-bill with annualized yield, because it
> is
> > a short rate, then is there any wrong? Can you provide any official link
> to
> > get daily US overnight Rate on net?
> >
> >
> >
> > However your explanation on Bond is not clear : "... reproduce the
> payoffs
> > by reinvesting proceeds of a short tenor bill into the forward term
> > structure". Could you please little bit more elaborate on that? The
> > language used here seems to be more difficult to me L
> >
> >
> >  ------------------------------
> >
> > *From:* bogaso.christofer [mailto:bogaso.christofer@gmail.com]
> > *Sent:* 29 December 2008 03:23
> > *To:* 'r-sig-finance@stat.math.ethz.ch'
> > *Subject:* Newbie question on risk free Interest Rate
> >
> >
> >
> > Hi,
> >
> >
> >
> > I would like to ask one newbie question on risk free interest rate. This
> is
> > the essential part to price any financial derivatives, like options,
> > Interest Rate only [IO] strip etc. My question is standing at time "t"
> which
> > risk free interest rate I should consider? 3 month, 6 month, 10 year
> t-bill
> > or t-bond ? for example suppose, I need to price a call option using BS
> > formula, whose remaining life time is 2 years and another option whose
> life
> > time is 5 months. Which interest rate I need to take to value those 2
> > options? After some goggling it is suggested to take 3 month t-bill as
> risk
> > free rate. What is the logic behind that?
> >
> >
> >
> > Again suppose, an Investor is to purchase an IO strip for 7 years, on a
> 10
> > years mortgage. In this case, I saw one book [by Cuthbertson], suggested
> to
> > take annual yield on 10-year t-bond to calculate NPV of all future
> Interest
> > payment against mortgage. However again it did not say why to take
> 10-year
> > bond not, 3-month t-bill.
> >
> >
> >
> > Can anyone here please clarify me on above doubts? Your help will be
> highly
> > appreciated.
> >
> >
> >
> > Thanks and regards,
> >
>
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>
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