personally, I use the rates that is for the particular maturity. eg if its
a 2.5month EUR call USD put, do an interpolation (cubic or linear - its your
preference) on the 1 and 3 month EUR and USD rates. typically i will use the
interbank rates for short end and the swaps for the long end.
having said that, the real impact of short dated (<1yr) options (and
therefore short dated rates) are pretty low. the issue only arise if you are
concerned with long dated options.
the most liquid and developed option markets are the spot forex markets. you
may want to consult an fx option market maker for real world practice.
>
>
> On Jun 1, 2009, Bogaso wrote:
>
> any view pls?
>
>
> Bogaso wrote:
> >
> > 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
> > price.
> >
> > -----Original Message-----
> > From: glenn [mailto:g1enn.roberts@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.
> >
> > Glenn
> >
> >
> > On 28/12/2008 21:53, "bogaso.christofer"
> > wrote:
> >
> >> 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,
> >>
> >>
> >> [[alternative HTML version deleted]]
> >>
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