Question

1a. For a stock trading at $50 with 15% volatility and 2% risk free interest rate, find the prices of a one month put and call options with a strike price of $50. b. Determine the effect on both the put and call of increasing the strike price to $55 Determine the effect of doubling the time to maturity

show work, step by step and explain please. no excel.

Answer 1

a)price of call and put options are $7.916 and $0.9536

b)due to increase in strike price to $55 the price of call and put options changed to $0.0045 and $2.4584

c)due to doubling time of maturity the prices of call and put options changed to $10.41 and -$0.6560

NOTES:

Solution was solved using normal distribution , logerthemic and exponential tables.
C asing Same blact schale del |b asing Same black-Scholes model Clven, E (strike price) 5s,Ssotmonth LER olasali) 15% e 1oo167 From above fomulae +002+ .225 10g(e.909)+o-0026 15 Co.2885 O.D4 S3 0s O.0943 +O.0026 O.O43305 Oroys3es -2.1175 logfo.g09)+0.02-0-0225 de o.0943 + 0.000 729 T O.043305 o-ISCo. 288) =-2.1607 sexNfa-es paite of tau 50 x N f2-1175)-55 xNfa1607) 50xNteo Treol67 sox (o.07)- 54.908x (0-0I54) C.85-0.84Ss 0.0045 Prce of put XN2160)- SxN(21125) 7Co/ 67 e 54.908 x (04846)-sOx (o-48 30) 26.608y- 24.15 2.4584

Sold-atberueer 9 C) using Same blact -Scholes model JE -0.y082 E 50, S= $50, t 2months aiven ,-2% 9 e*t= /0066 0+(o-03125)1n d = O.0052) 0.0851 o.5 (0.4082) 0.06123 (o02-0-0125) 2/ OIS(0.4082 d, = O.001458 O.0238 O.06123 rite et Cal S0XN0-08si)- xNo-0238) 50 (o-3023)-19.672200v 49-6722 Price of puet SoxNa238)-50XN-o.08s) 1.0066 9.6722 Xfo-45- 5ax(a4601) 22.35249 23.0085 f0.6560

Answer (a) using Black-Scholes Fomula Civen eta00/6 =Q%S$5o, E(Strikeprice) =50,t-1month 15%, O-022s d, ELS(o.2887) otfo03/25) O.43305 + otfo.02-0.042) G t Doy3305 = 0.0168 Price a Cau= XN(d SOXN (0.060) So AL0.06) - SOX o.Q257 50 KO.0675 1.00167 7.9/6 11-285- 3.369 xNd)S x N(-,) Price put 1 ert x O.4960-50 x0.4761 3C. 24.7586- a3.805 DO167 Notos N/d) og(x)lo tatle value ex -$0.9536 -Stands For Normal distribution tade Vaues Y8cu.c :Stands for exponential table values