Question

A 1-year European call and put options on a non-dividend paying stock has a strike price of 80. You are given: (i) The stock’s price is currently 75.
(ii) The stock’s price will be either 85 or 65 at the end of the year.
(iii) The continuously compounded risk-free rate is 4.5%.

(a) Determine the premium for the call.

(b) Determine the premium for the put.

Answer 1

ANSwey : Strike Price = 80 Current stock price = 75 Stock price can Increase by 85 cor Decrease by 65 Rifk free rate : 4.st. price can option to *P"gre fers probability of Increaziy Stock *(1-P) "oretegy to probability of decreasy stock price 85(P) + 65(1-P) - 75 + 75 x 4.5%. 850 + 65-650 - 25+ 3.375 200 = 78.375 – 65 P = 0.66875 CI-P) = 0. 33125 Su= max (Su-x,0) Su = max (85-80,0) su = 5 sa So Sd = = > max max (Sa-x, o) (65-80,0) 0

premium of it call option p. Su + C1-p) 0.66875 x 5 + 0.33125 x 0 (uasa 3.34375 2. of & call option 1 year premium after 4- 3.34375 AS OF Now at year = 3.34315 (HUS) 3 pobol wat foto 2raop. sultys toores 12 1.045 Premium in call option - 3. 19976 put option put option is exercised when Strike price is more than the stock price Imarket price at 2 Expiry. odgo Tue 40 minuta → The calculation of probability is Same of - Call option. - - Now, Su = max (x-Su 10) Su & max (80-85,0) Su - O Sa = max (x - Sa 10) = max (80- 65,0) Sa = 15

6) Premium of put option. = pisu) + C1-P) Sd 9-13 with = 0.66875 X0 + 0.33125 x 15 d. 2154 0+ 4.96875 4.96875 A / B gr. premium of put option after one year 4.96875 wote 4.96875 premium - as of now, Today = 4.96875 present valle notoo long S factor of 4-5 .96875 ir 4 Proy own orta bezeroxa (1 Drog transfer both grit store.ao exs Cl +4.54) 204.96875 090492 35 yilidadocy z mosta 78 premium of put option. 1045 to = 4.75478 orico lo 2 won O xom (0.28 - 03) on je (o, a naron (0.23 - 03) om