show how in step 3 the binominal model is derived

(option premium now + stock price now + borrow deposit now =0 to be the formula for the option premium equation)

1. The portfolio is riskless if it gives a constant value => riskless if -Cd + da S. Cu+ ua S=>+ua S-da S- Cu - Cd=> a (u S - ds ) = Cu-Cd a = (Cu-Cd)/(u - d) S Hedge ratio! 2. The portfolio is worthless in the future if -Cd + da S = something =- Cu + ua S# something = 0. Will be that if we borrow/ deposit the present value of the future cash-flow, i.e. (-Cd + da S)/R or (- Cu + ua S)/R, where R=(1+rf). 29 Binomial Model (Cont'd) 3.) The no-arbitrage condition requires that such a portfolio should cost zero today: Option premium now . + stock price now + borrow/ deposit now = 0 => gives the option premium C9+(1-4) R -as (- Cd + da S)/R c: c where Red u-d 9 = The Binomial model