1. Consider a stock that currently sells for $60. Over the next six months, the stock will either increase to $90 or decrease to $42. Semiannual risk-free rate is 2%. (Use replicating portfolio approach.)

1. What is the value of a European call option on this stock with an exercise price of $63 and expiration in six months?
2. What is the value of a European put option on this stock with an exercise price of $63 and expiration in six months?
3. Set the put-call parity between the options in parts a and b, and see if the parity holds. [Optional]

2. Consider a stock that currently sells for $40. Over each of the next two six-month periods, the stock will either increase by 15% or decrease by 15%. Semiannual risk-free rate is 3%. (Use risk-neutral probability approach.)

1. What is the value of a European call option on this stock with an exercise price of $36 and expiration in one year?
2. What is the value of a European put option on this stock with an exercise price of $36 and expiration in one year?
3. Set the put-call parity between the options in parts a and b, and see if the parity holds. [Optional]

3. International Business Machines Corps stock closed at $94.15 on March 27, 2021. Stocks daily volatility over the past year was 2.482%. Companys quarterly dividend is $0.50 per share. Risk-free rate is 5%. (Use Black-Scholes approach.)

1. Calculate the value of a European call option on this stock with an exercise price of $100 and expiration of Oct 21 (Hint: Option expire on the 3^rd Friday of October of 2021 use this to count the number of days to expiration, and then convert that to the years, i.e. T).
2. Calculate the value of a European put option on this stock with an exercise price of $100 and expiration of Oct 21 (i.e. 3^rd Friday of October of 2021).
3. Set the put-call parity between the options in parts a and b [Optional].