Hi: When you say the 'black" formula, I think you might be talking about the martingale valuation approach as opposed to the replication approach ? if that's the case, then what changes in the expectation ( in the martingale approach ) is the distribution of how the price evolves under the risk neutral probability distribution. i.e: the distribution that makes the price a martingale .<br /> <br /> this doesn't have anything to do with the factor that you discount with to get the present value. as long as the r that you discount back with is the same r that you take the expectation of P with respect to, then r can be anything you want. they use r but it's just a parameter . in fact, for me , using r confuses the derivation. i just think of r as the parameter in the transformed diffusion that makes S a martingale . in the continous hedging derivation, the r<br /> that they used to hedge ends up being the same as the "risk free r" in the martingale derivation because in the<br /> hedging derivation they hedge the stock process to create a risk free portfolio and end up with the differential<br /> equation whose solution is BS.<br /> <br /> someone on this list that deals with options more than me , please feel free to correct me on this or say more because it's been a long time since i looked at this material and my memory/thinking could be wrong. I just replied because this is the second time I saw this question and I didn't see a reply.<br /><br /><br /> <br /><br /><p>On Jun 1, 2009, <strong>Bogaso</strong> <bogaso.christofer@gmail.com> wrote: </p><div class="replyBody"><blockquote style="border-left: 2px solid #267fdb; margin: 0pt 0pt 0pt 1.8ex; padding-left: 1ex"><br />any view pls?<br /><br /><br />Bogaso wrote:<br />> <br />> Hi, I have come across one more question. I understood that for BS options<br />> pricing, I should take short rate i.e. overnight rate because BS derive<br />> option price through some replicating portfolio which is changed<br />> instantaneously. However if I price an instrument using Black formula,<br />> wherein only the distribution of underlying at maturity period is<br />> considered<br />> i.e. in this case there is no replicating portfolio story, shouldn't I<br />> consider risk free rate for longer horizon i.e. a rate whose maturity<br />> period<br />> exactly matches with the life of the instrument?<br />> <br />> I mean to say, under Black's framework, one only needs to calculate<br />> expected<br />> value of the instrument like E[max(0, S[T] - K)] at maturity and then to<br />> calculate the present value of that. In this case there is nothing abt<br />> replicating portfolio. Therefore I feel that to calculate PV I should<br />> consider LIBOR with maturity [o, T]. <br />> <br />> What you feel on that? If I am correct i.e. if I price same option using<br />> BS<br />> and Black, there must be some fundamental difference in theoretical option<br />> price.<br />> <br />> -----Original Message-----<br />> From: glenn [mailto:<a href="mailto:g1enn.roberts@btinternet.com" target="_blank" class="parsedEmail">g1enn.roberts@btinternet.com</a>] <br />> Sent: 29 December 2008 17:33<br />> To: bogaso.christofer<br />> Subject: Re: [R-SIG-Finance] Newbie question on risk free Interest Rate<br />> <br />> Further to Mahesh's answer Christofer, think of it like this;<br />> <br />> The rate in the BS calculation represents a rate that any portfolio<br />> consisting of an option and the delta equivalent of the underlying (in<br />> your<br />> example a swap maybe) MUST earn. Think about how long the portfolio will<br />> remain delta neutral (risk free) for before a re-balence is needed. That's<br />> the rate you want i.e the short rate.<br />> <br />> Glenn<br />> <br />> <br />> On 28/12/2008 21:53, "bogaso.christofer" <<a href="mailto:bogaso.christofer@gmail.com" target="_blank" class="parsedEmail">bogaso.christofer@gmail.com</a>><br />> wrote:<br />> <br />>> Hi,<br />>> <br />>> <br />>> <br />>> I would like to ask one newbie question on risk free interest rate. This<br />> is<br />>> the essential part to price any financial derivatives, like options,<br />>> Interest Rate only [IO] strip etc. My question is standing at time "t"<br />> which<br />>> risk free interest rate I should consider? 3 month, 6 month, 10 year<br />> t-bill<br />>> or t-bond ? for example suppose, I need to price a call option using BS<br />>> formula, whose remaining life time is 2 years and another option whose<br />> life<br />>> time is 5 months. Which interest rate I need to take to value those 2<br />>> options? After some goggling it is suggested to take 3 month t-bill as<br />> risk<br />>> free rate. What is the logic behind that?<br />>> <br />>> <br />>> <br />>> Again suppose, an Investor is to purchase an IO strip for 7 years, on a<br />>> 10<br />>> years mortgage. In this case, I saw one book [by Cuthbertson], suggested<br />> to<br />>> take annual yield on 10-year t-bond to calculate NPV of all future<br />> Interest<br />>> payment against mortgage. However again it did not say why to take<br />>> 10-year<br />>> bond not, 3-month t-bill.<br />>> <br />>> <br />>> <br />>> Can anyone here please clarify me on above doubts? Your help will be<br />> highly<br />>> appreciated.<br />>> <br />>> <br />>> <br />>> Thanks and regards,<br />>> <br />>> <br />>> [[alternative HTML version deleted]]<br />>> <br />>> _______________________________________________<br />>> <a href="mailto:R-SIG-Finance@stat.math.ethz.ch" target="_blank" class="parsedEmail">R-SIG-Finance@stat.math.ethz.ch</a> mailing list<br />>> <a href="https://stat.ethz.ch/mailman/listinfo/r-sig-finance" target="_blank" class="parsedLink">https://stat.ethz.ch/mailman/listinfo/r-sig-finance</a><br />>> -- Subscriber-posting only.<br />>> -- If you want to post, subscribe first.<br />> <br />> _______________________________________________<br />> <a href="mailto:R-SIG-Finance@stat.math.ethz.ch" target="_blank" class="parsedEmail">R-SIG-Finance@stat.math.ethz.ch</a> mailing list<br />> <a href="https://stat.ethz.ch/mailman/listinfo/r-sig-finance" target="_blank" class="parsedLink">https://stat.ethz.ch/mailman/listinfo/r-sig-finance</a><br />> -- Subscriber-posting only.<br />> -- If you want to post, subscribe first.<br />> <br />> <br /><br />-- <br />View this message in context: <a href="http://www.nabble.com/Re%3A-Newbie-question-on-risk-free-Interest-Rate-tp23660753p23815043.html" target="_blank" class="parsedLink">http://www.nabble.com/Re%3A-Newbie-question-on-risk-free-Interest-Rate-tp23660753p23815043.html</a><br />Sent from the Rmetrics mailing list archive at Nabble.com.<br /><br />_______________________________________________<br /><a href="mailto:R-SIG-Finance@stat.math.ethz.ch" target="_blank" class="parsedEmail">R-SIG-Finance@stat.math.ethz.ch</a> mailing list<br /><a href="https://stat.ethz.ch/mailman/listinfo/r-sig-finance" target="_blank" class="parsedLink">https://stat.ethz.ch/mailman/listinfo/r-sig-finance</a><br />-- Subscriber-posting only.<br />-- If you want to post, subscribe first.<br /></blockquote></div>