Come to the blackboard Master Jones and solve the equation, step by step.Yes. Yes, I do.The main thing is have you understood where the integral comes from and how that integration by parts was achieved?
From BS to heat Pde
https://www.math.tamu.edu/~stecher/425/ ... uation.pdf
on the 2nd line stating upfront that [$]V(0,t) = 0[$] is so wrong.
The author seems not to be aware of Bachelier. But it is inconvenient that the mathematical object of Brownian motion was first developed in the context of option pricing.
Two or three lines? I'd like to see them. And no more copying from other boys' work this time!From BS to heat Pde
https://www.math.tamu.edu/~stecher/425/ ... uation.pdf
on the 2nd line stating upfront that [$]V(0,t) = 0[$] is so wrong.
What have we here, laddie? Mysterious scribblings? A secret code? Three pages later we encounter an answer that is off by an odd factor of [$] e^{ \frac{\sigma^2}{8}} [$]. To a problem that would generously take two lines to answer with a probabilistic approach.
I second that. Just make sure he does his 3rd conjugation Latin verbs as well.Two or three lines? I'd like to see them. And no more copying from other boys' work this time!From BS to heat Pde
https://www.math.tamu.edu/~stecher/425/ ... uation.pdf
on the 2nd line stating upfront that [$]V(0,t) = 0[$] is so wrong.
What have we here, laddie? Mysterious scribblings? A secret code? Three pages later we encounter an answer that is off by an odd factor of [$] e^{ \frac{\sigma^2}{8}} [$]. To a problem that would generously take two lines to answer with a probabilistic approach.
That note had two partsbearish is correct. It's a two-liner at best:
Line 1: from the BS formula under std notation, it is immediate that [$]C_K = -e^{-r T} \Phi(d_2(K)) = -e^{-r T} E[1_{S_T>K}][$].
Line 2: The problem at hand is [$]3 e^{-r T} (E[1_{S_T>1}] - E[1_{S_T>2}]) =3 e^{-r T} ( \Phi(d_2(1)) - \Phi(d_2(2)))[$]
page 3 of the link contain two typos.
Only saw this now.Probabilistic thinking in finance is an example of the Sapir-Whorf Hypothesis.
Sounds like an excellent place to take out a 20-year loan!Only saw this now.Probabilistic thinking in finance is an example of the Sapir-Whorf Hypothesis.
I wonder how the Hopi tribe of Arizona would view first hitting time seeing that they have no words for time, past, present or future.