Option payoffs and profits at expiration to assess what an option is worth. The binomial option pricing model: making assumption that at the end of the next period the stock price has only 2 possible values. = # of shares of stock we purchase: b = investment in the risk-free asset (if b<0, means that rather than investing in the risk-free asset, the replicating portfolio requires borrowing b at the risk-free rate) 62 + 1. 05 b = 10 in down state , value must be sh : 42 + 1. 05 b = 0 ( 62 + 1. 05 b = 10) ( 42 + 1. 05 b = 0) = 20 = 10 subtracting down state from up state. C0 (call today) = value of replicating portfolio = value of 0. 5 shares amount borrowed = 0. 5x52-20 =6 thus price of call today = .