Question

3. Assuming that a one-year call option with an exercise price of $28 is available for the stock of the DEW Corp., consider the following is a two-period price tree for DEW stock over the next year: You also know that the risk-free rate is RFR 5 percent per subperiod (or 10.25 percent annualized).

a. If the sequence of stock prices that DEW stock follows over the year is $30.00, $33.00, and $29.70, describe the composition of the initial riskless portfolio of stock and options you would form and all the subsequent adjustments you would have to make to keep this portfolio riskless.

b. Given the initial DEW price of $30, what are the probabilities of observing each of the three terminal stock prices in one year? (Hint: In arriving at your answer, it will be useful to consider (1) the number of different ways that a particular terminal price could be achieved and (2) the probability of an up or down movement.)

c. Use the binomial option model to calculate the present value of this call option.

d. Calculate the value of a one-year put option on DEW stock having an exercise price of $28; be sure your answer is consistent with the correct response to part (c).

Styles Paragraph ab De I3 I 4 I 5 1 6- I 1 I 2 PORATE INVESTMENT ANALYSIS hapter 16: Problems 3(a-d), 4(a-d), 6(a-c), and 9(a-b) Assuming that a one-year call option with an exercise price of $28 is available for the tock of the DEW Corp., consider the following is a two-period price tree for DEW stock ver the next year: Now S1 One Year 36.30 33.00 29.70 30 27.00 24.30 You also know that the risk-free rate is RFR 5 percent per subperiod (or 10.25 percent annualized). a. If the sequence of stock prices that DEW stock follows over the year is $30.00, $33.00, and $29.70, describe the composition of the initial riskless portfolio of stock and options you would form and all the subsequent adjustments you would have to make to keep this portfolio riskless. b. Given the initial DEW price of $30, what are the probabilities of observing each of the three terminal stock prices in one year? (Hint: In arriving at your answer, it will be useful to consider (1) the number of different ways that a particular terminal price could be achieved and (2) the probability of an up or down movement.) c. Use the binomial option model to calculate the present value of this call option. d. Calculate the value of a one-year put option on DEW stock having an exercise price of $28; be sure your answer is consistent with the correct response to part (c) DELL :253 17 5494:100 100008 2 308 2 548 FCU: (6 ST: CAP:

Answer 1

A. First create bionomial Tree in following way

Page DATE A first we have to create Bionomice node Suu = Surų 3073-334 Su-Soxit 33 - 30x1.1 SUL = suxd 29.7 = 33x0,9 S = Soxd where 27-30x0.90 so current Steen su stock price if price go up su Sixd SL Stock Pilce 2 90_down 20.3 = 27 vag Suy - stoen Puce if shat go up and engcun go up Su= sloch Price if first go up and down SuLL Stoen price go w down and again up u= de to go up down factar IF Stock Price feictor Is Stock Price Su = 33 - lol So 30 u = u 1.1

B. find probability using following formula.

upwant Find the Probabirity probability of of dow wurd und P= stock Price will Probability that go up Probablity that 9 = sheen Price colle a doun P = CHRI-d where 7 Cltoos-0.9 c Sub Period) R = Rush free Rute d = downward Factor U = Upwant fuctes on - 0.15 0.20 O-2025 ora - P = 9 = 0.75 P = 1-0.75 = 0.25

C find the current value of call option V_c by following way.

CATE Bionomical tree nolio, 7 36.3 = Max (36.3-2010 V (PxVcuu / COX Veu = (0-75 839 CO2X1.7) CO 3 3 Vey - 6.33 Vani - 8.3 29.7 Ver mark (29.-289, 1.7 Ve= 27 Velveuw C 9 X Vowth 24.3. 0) Vezi Max C 24.3-27,0 C1+205) - 1.21 CV Value of call option - Max (3-X,o) - Stock Price x exordse puce where tu pa probablut H pulp co (P X Vew CP x Ven) CHR = (.75 X6.332 (0-25 V1.2 DI CHROS) = 4.812 Allepuhiirt /of down q fthephili? pa RF Rute

D.find the current value of put option V_p by following way.

Bionomial free 363 You o 33 Z Powe 29.7 Vouro 201.3 OLL 3-7 Pu V yolue of Vouu = Vou os vou - - Vou - Cant option - Max CX-57,0) mux (28-36.37,0 = 0 Max (28-29.7),0) = 0 Mex (28-24.3,0 = 3.7 You - (Px Vpun (9 %(vaw - (0.75X0) (0.25x0) = o (1.05) l Vpe=(Px veul) CqXVPL)-COASKO) (0.23X3.7.)= (0,88 ना - (Px Npw (9x Upide (0.25 x0)(0.2 x 0.881) CHAS where Vp - Vermie ot = 2097 = 0.217 ਮਚ