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 May 27th, 2016, 05:23 PM #1 Member   Joined: Sep 2013 Posts: 83 Thanks: 0 American Put Options - Journal Article Help In the article "The American Put Option and Its Critical Stock Price" Bunch and Johnson (2000), the author posed this expression as a representation of an American put option: $\displaystyle P= p+ \int_{0}^{T} rXe^{-rt}N(-d_{2}(S,Sc,t))dt$ where $\displaystyle d_{2}(S,Sc,t) = \frac{\log (S/Sc) +(r-\frac{1}{2}\sigma^2 )}{\sigma \sqrt{t}}$ Now in the article, they say that this can be shown to yield the following: $\displaystyle \frac{Sc}{X}=e^{(r+(1/2)\sigma ^2)\tau -g\sigma \sqrt{\tau }}$ where $\displaystyle \tau \equiv T-t$ $\displaystyle g=\pm \sqrt{2\log\frac{\sigma ^2}{\frac{2r}{\sqrt{a}}x\, \log\, xe^{-a(r+(1/2)\sigma ^2)^2\tau /(2\sigma ^2)}}}$ and $\displaystyle \gamma \equiv \frac{2r}{\sigma ^2}$ $\displaystyle a=1-\frac{A}{1+\frac{(1+\gamma )^2}{4}\sigma ^2\tau }$ $\displaystyle A=\frac{1}{2}\left ( \frac{\gamma }{1+\gamma } \right )^2$ $\displaystyle x= \frac{X}{Sc}$ Question is how did they do that? Note: I have solved this once, but I threw the piece of paper , don't ask me why... Last edited by skipjack; May 27th, 2016 at 09:26 PM. Tags american, article, journal, options, put Thread Tools Show Printable Version Email this Page Display Modes Linear Mode Switch to Hybrid Mode Switch to Threaded Mode Similar Threads Thread Thread Starter Forum Replies Last Post Ku5htr1m Differential Equations 1 May 31st, 2016 12:02 PM testtrail429 Algebra 2 April 11th, 2013 11:11 AM soroban New Users 7 April 1st, 2013 07:33 PM laurita Economics 0 January 28th, 2013 06:22 AM r-soy Physics 2 February 18th, 2012 01:00 PM

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