Probability downward factor=1/1.2=0.8333
Interest rate factor for period 1(R1)=1+1/39=1.025
Interest rate factor for period 2(R2)=1+1/19= 1.052
Probability of upward price movement for period 1= R1-d/(u-d)=(1.025-0.8333)/(1.2-0.8333)=52.27%
Probability of downward price movement for period 1=(1-52.27%)=47.73%
Probability of upward movement for period 2= R2-d/(u-d)=(1.052-0.8333)/(1.2-0.8333)=59.64%
Probability of downward movement for period 2= 1-59.64%=0.4036=40.36%
Price of stock after period 1 is either 150*1.2=180 or 150*0.8333=125
Price of stock after period 2 is either 180*1.2=216 or 180*0.8333=150 or 125*1.2=150 or 125*0.8333=104.15
So, expected payoff for a call option with strike price of 153= 52.27%*59.64%*(216-153)+0+0=$19.63
Present value of expected value of call option= 19.63/(1.025*1.052)=$18.20
Value of call option is $18.20
b. Similarly, expected payoff for a put option with 153 strike price= 0+(153-150)*52.27%*40.36%+(153-150)*47.73%*59.64%+(153-104.15)*47.73%*40.36%=$10.89
Present Value of expected payoff= 10.89/(1.025*1.052)=$10.099
Value of put option is $10.099
1) In a two period model, a stock starts at 150. It either goes up by...
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A stock currently sells for $50. In six months it will either rise to $60 or decline to $45. The continuous compounding risk-free interest rate is 5% per year. Using the binomial approach, find the value of a European call option with an exercise price of $50. Using the binomial approach, find the value of a European put option with an exercise price of $50. Verify the put-call parity using the results of Questions 1 and 2.
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