Question

(1 point) A stock currently trades at $44, and the volatility of its return is 46%. The continuously compounded rate of interest is 3%. Consider a call option struck at $49, with 100 days to expiration (recall that there are 251 trading days in one year). a) What is the price of the option (rounded to the nearest cent)? Answer = $ b) What is the option's delta (rounded to four decimal places)? Answer = c) Use your answer from (b) to estimate the value of the option tomorrow, assuming the stock is trading at $45.05 at that time? Answer = $ d) What is the exact value of the option tomorrow, assuming the stock is trading at $45.05 at that time? Answer = $ [Note: Use software to compute the values of the normal CDF, not the table.]

(1 point) A stock currently trades at $44, and the volatility of its return is 46%. The continuously compounded rate of interest is 3%. Consider a call option struck at $49, with 100 days to expiration (recall that there are 251 trading days in one year).

a) What is the price of the option (rounded to the nearest cent)?

b) What is the option's delta (rounded to four decimal places)?

c) Use your answer from (b) to estimate the value of the option tomorrow, assuming the stock is trading at $45.05 at that time?

d) What is the exact value of the option tomorrow, assuming the stock is trading at $45.05 at that time?

Answer 1

c: value of call option

r: risk free rate = 3%

k: strike price = 49

t: time to expiry = 100days = 100/252 years = 0.4 years

s(sigma) volatility = 46%

S stock price = 44

c = S*N(d1) -K*e^(-r*t)*N(d2)

d1 =

+(1+0.5s) * t)/(5 * Vt)

d1 = (-0.1076+(0.03+0.5*.46*.46)*0.4)/(.46*0.4^0.5)

d1 = -0.183

d2 = = -.183 - .46*0.4^0.5 = -0.474

+ *S – IP

N(d1) normsdist function = 0.427

N(d2) = 0.318

(a)c = 44*0.427 - 49*0.319*e^(-0.03*0.4) = 18.79 - 15.45 = 3.34 ie price of call option

(b) delta = N(d1) = 0.427

(c) Change in value of option =

As * Nd1)

where delta s is change in stock price

Change in option price = (45.05 - 44)*0.427 = 0.448

New option price = 3.34 + 0.448 = 3.788