Question

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)

Answer 1

stock of Company ABC 5 ). ( 202012/24 21:32 124. 27 9-1-0.5 149.5 Kz @1 ( exercise price Now using above diapram calculate the pay off of European call option. we will the stock price > Strike or exercise exercised otheowice it will be lapsed. Now How we will use back ward Calculation tion of pay off for each NODE.

NODED pay off = 50.5 NUDE NODE E -pay off = o Clapsed NODE F y pay off a o clapsed) 2020 0 23x0.5 NODE B - pay off = NODE C y pay off poru = 0x05 NODE Aty is lay ass = 1 olne NODE B PV of pross pay off 50.5X0.5 + OX0.50 24.27 - 1.04 MODE C PU of gross pay of oxor+ 0x0.5 1.04 = oooh

our way NODE A pu of pross pay off 2020/2124 21:32 ROLE Win Rox 0.5+ 0x0.5 1.04. TEL/ESTMENT price of the option (so sxo.5 + Ler o x 0. 5 e -0.4 XI 2 - 17.42 MERAY
we will similarly do for the american call option but the difference here will be is that we will compare the payoff with the intrinsic value so that we can choose the greater value for the payoff.