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.


closed as off-topic by LocalVolatility, skoestlmeier, AdB, amdopt, Bob Jansen May 19 at 12:18

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  • $\begingroup$ It is the riskneutral probability. What do you know about riskneutral valuation? $\endgroup$ – Andrew May 11 at 16:45
  • 1
    $\begingroup$ 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 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 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 at 17:47