[R-SIG-Finance] Newbie question on risk free Interest Rate

bogaso.christofer bogaso.christofer at gmail.com
Thu May 21 23:39:45 CEST 2009

Hi, I have come across one more question. I understood that for BS options
pricing, I should take short rate i.e. overnight rate because BS derive
option price through some replicating portfolio which is changed
instantaneously. However if I price an instrument using Black formula,
wherein only the distribution of underlying at maturity period is considered
i.e. in this case there is no replicating portfolio story, shouldn't I
consider risk free rate for longer horizon i.e. a rate whose maturity period
exactly matches with the life of the instrument?

I mean to say, under Black's framework, one only needs to calculate expected
value of the instrument like E[max(0, S[T] - K)] at maturity and then to
calculate the present value of that. In this case there is nothing abt
replicating portfolio. Therefore I feel that to calculate PV I should
consider LIBOR with maturity [o, T]. 

What you feel on that? If I am correct i.e. if I price same option using BS
and Black, there must be some fundamental difference in theoretical option

-----Original Message-----
From: glenn [mailto:g1enn.roberts at btinternet.com] 
Sent: 29 December 2008 17:33
To: bogaso.christofer
Subject: Re: [R-SIG-Finance] Newbie question on risk free Interest Rate

Further to Mahesh's answer Christofer, think of it like this;

The rate in the BS calculation represents a rate that any portfolio
consisting of an option and the delta equivalent of the underlying (in your
example a swap maybe) MUST earn. Think about how long the portfolio will
remain delta neutral (risk free) for before a re-balence is needed. That's
the rate you want i.e the short rate.


On 28/12/2008 21:53, "bogaso.christofer" <bogaso.christofer at gmail.com>

> Hi,
> I would like to ask one newbie question on risk free interest rate. This
> the essential part to price any financial derivatives, like options,
> Interest Rate only [IO] strip etc. My question is standing at time "t"
> risk free interest rate I should consider? 3 month, 6 month, 10 year
> 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
> 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
> 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
> take annual yield on 10-year t-bond to calculate NPV of all future
> 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
> appreciated.
> Thanks and regards,
> [[alternative HTML version deleted]]
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