Test

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c) Replicating portfolio by borrowing B amount cash to buy Delta underlying (either call option or put option in this case)
For ConC:
To make sure the portfolio has the same payoffs in T=1 and thus ConC price should be same as the price of this portfolio at T=0. The portfolio price at T=0 is Delta * C(0) – B.
Delta * Cu – B (1+r) = max (Cu-X, 0)
Delta * Cd – B (1+r) = max (Cd-X, 0)

Cu = 17.57, Cd = 0, X =0.  Delta = 0.4315, B = 0  The price of Portfolio is 0.4315*11.02 = 4.75 which is matched with ConC.

For ConP:
To make sure the portfolio has the same payoffs in T=1 and thus ConP price should be same as the price of this portfolio at T=0. The portfolio price at T=0 is Delta * P(0) – B.
Delta * Pu – B (1+r) = max (Pu-X, 0)
Delta * Pd – B (1+r) = max (Pd-X, 0)

Pu = 6, Pd = 25.93, X =0.  Delta = 0.7993, B = 4.70176  The price of Portfolio is 0.7993*12.92-4.70176 = 5.62 which is matched with ConP.

If share price goes up call option price goes up( because the payoff in each node of the call option tree goes up when the underlying share price goes up) and ConC goes up ( because the payoff of each node of the ConC tree goes up when the underlying call option price goes up).

If share price goes up put option price goes down (because the payoff in each node of the put option tree goes down when the underlying share price goes up) and ConP goes…...

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