ABC's stock price is 88 and in 3 months it will either increase (probability is 50%) by 25% or fall by 25%. Then again over the next 3 months (i.e. from month 3 to month 6) it will again increase (probability is 50%) by 25% or fall by 25%. The risk- free rate for 3 months is constant and equal to 2% (not annualized). a) Find the price of a 6-month European call on ABC stock with exercise price of 87. Use replication portfolio approach. (20 points) b) Find the price of a 6-month American call on ABC stock with exercise price of 87. (10 points) c) Find the price of a 6-month European put on ABC stock with exercise price of 87. Use risk-neutral valuation approach. (20 points) d) Find the price of a 6-month American put on ABC stock with exercise price of 87. Use risk-neutral valuation approach. (10 points) e) Check Put-Call parity for European options. (10 points) ABC's stock price is 88 and in 3 months it will either increase (probability is 50%) by 25% or fall by 25%. Then again over the next 3 months (i.e. from month 3 to month 6) it will again increase (probability is 50%) by 25% or fall by 25%. The risk- free rate for 3 months is constant and equal to 2% (not annualized). a) Find the price of a 6-month European call on ABC stock with exercise price of 87. Use replication portfolio approach. (20 points) b) Find the price of a 6-month American call on ABC stock with exercise price of 87. (10 points) c) Find the price of a 6-month European put on ABC stock with exercise price of 87. Use risk-neutral valuation approach. (20 points) d) Find the price of a 6-month American put on ABC stock with exercise price of 87. Use risk-neutral valuation approach. (10 points) e) Check Put-Call parity for European options. (10 points)