The Black-Scholes Model. Randomness matters in nonlinearity . An call option with strike price of 10. Suppose the expected value of a stock at call option’s maturity is 10. If the stock price has 50% chance of ending at 11 and 50% chance of ending at 9, the expected payoff is 0.5.
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ƒ = S – K e–r (T – t )
c = 3 S0= 31
T = 0.25 r= 10%
K =30 D= 0