Question: The price of a stock is 100. With equal probabilities, it either goes up to 130 or down to 70. What is the price of a 1 year call option with exercise price 100. Risk free rate is 5%.
Attempt: I use black scholes.
- Given: $Su=130. Sd=70.rf=5% S_0=100$
- $Cu=max(0,130-100)=30. Cd=max(0,70-100)=30$
Now, $$HedgeRatio = (30-0)/(130-70)=1/2$$ $$B=(Cd-Sd \cdot HedgeRatio)/(1+rf)=(0-70/2)/(1.05)=-(33+1/3)$$ So the price of the call option is $$C_0=S_0*Hedgeratio+B= 100/2 -(33+1/3)=16+2/3$$ but it is wrong.