My question here is how is the probability of an up move calculated by $(1+Rf-D)\over(U-D)$ derived where Rf is the risk free rate, D is the down move factor and U represents the up move factor.

Kindly help me understand the derivation and where this formula comes from as this does not make any intuitive sense to me.

Thanks in advance.

  • $\begingroup$ It is the riskneutral probability. What do you know about riskneutral valuation? $\endgroup$ – Andrew May 11 '19 at 16:45
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    $\begingroup$ In a risk-neutral world the expected future asset price equals the forward price: $$p( \, US\,) +(1-p)(\,DS\, ) = S(1 + r_f) \implies p = \frac{1 + r_f - D}{U - D}$$ $\endgroup$ – RRL May 11 '19 at 17:12
  • $\begingroup$ @Andrew I am a newbie in the process of learning about valuation of options and other contingent claims and therefore has little to no knowledge about risk neutral valuation. $\endgroup$ – Aditya Jain May 11 '19 at 17:35
  • $\begingroup$ @RRL Thanks for the answer. I now understand the algebra behind the equation. Maybe reading further about Risk Netural probabilities will help me better understand it. $\endgroup$ – Aditya Jain May 11 '19 at 17:47