[R-SIG-Finance] [R-sig-finance] Newbie question on risk free Interest Rate
Bogaso
bogaso.christofer at gmail.com
Mon Jun 1 15:32:27 CEST 2009
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 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.
>
> Glenn
>
>
> On 28/12/2008 21:53, "bogaso.christofer" <bogaso.christofer at gmail.com>
> 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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