Question

The common shares of Twitter, Inc. (TWTR) recently traded on the NYSE for $21.70 per share. You have employee stock options to purchase 1,000 TWTR shares for $20.8 per share. The options expire in three years. Assume that the annualized volatility of TWTR stock is 88.6 percent and that the interest rate is 2.6 percent. (Assume the options are European options that may only be exercised at the maturity date.)

a. Is this option a call or a put?

• Call

• Put

b. Using an option pricing calculator such as the one at erieri.com/blackscholes, estimate the value of your TWTR options. (Round option value per share to 2 decimal places.)

c. What is the estimated value of the options if their maturity is six months instead of three years? (Round option value per share to 2 decimal places.)

d. What is the estimated value of the options if their maturity is three years, but TWTR’s volatility is 63.2 percent? (Round option value per share to 2 decimal places.)

Answer 1

a

Option is a call option

b

As per Black Scholes Model
Value of call option = (S)*N(d1)-N(d2)*K*e^(-r*t)
Where
S = Current price =		21.7
t = time to expiry =		3
K = Strike price =		20.8
r = Risk free rate =		2.6%
q = Dividend Yield =		0%
σ = Std dev =		89%
d1 = (ln(S/K)+(r-q+σ^2/2)*t)/(σ*t^(1/2)
d1 = (ln(21.7/20.8)+(0.026-0+0.886^2/2)*3)/(0.886*3^(1/2))
d1 = 0.845729
d2 = d1-σ*t^(1/2)
d2 =0.845729-0.886*3^(1/2)
d2 = -0.688868
N(d1) = Cumulative standard normal dist. of d1
N(d1) =0.801148
N(d2) = Cumulative standard normal dist. of d2
N(d2) =0.245453
Value of call= 21.7*0.801148-0.245453*20.8*e^(-0.026*3)
Value of call= 12.66

c

As per Black Scholes Model
Value of call option = (S)*N(d1)-N(d2)*K*e^(-r*t)
Where
S = Current price =		21.7
t = time to expiry =		0.5
K = Strike price =		20.8
r = Risk free rate =		2.6%
q = Dividend Yield =		0%
σ = Std dev =		89%
d1 = (ln(S/K)+(r-q+σ^2/2)*t)/(σ*t^(1/2)
d1 = (ln(21.7/20.8)+(0.026-0+0.886^2/2)*0.5)/(0.886*0.5^(1/2))
d1 = 0.401612
d2 = d1-σ*t^(1/2)
d2 =0.401612-0.886*0.5^(1/2)
d2 = -0.224885
N(d1) = Cumulative standard normal dist. of d1
N(d1) =0.656015
N(d2) = Cumulative standard normal dist. of d2
N(d2) =0.411035
Value of call= 21.7*0.656015-0.411035*20.8*e^(-0.026*0.5)
Value of call= 5.8

d

As per Black Scholes Model
Value of call option = (S)*N(d1)-N(d2)*K*e^(-r*t)
Where
S = Current price =		21.7
t = time to expiry =		3
K = Strike price =		20.8
r = Risk free rate =		2.6%
q = Dividend Yield =		0%
σ = Std dev =		63%
d1 = (ln(S/K)+(r-q+σ^2/2)*t)/(σ*t^(1/2)
d1 = (ln(21.7/20.8)+(0.026-0+0.632^2/2)*3)/(0.632*3^(1/2))
d1 = 0.65728
d2 = d1-σ*t^(1/2)
d2 =0.65728-0.632*3^(1/2)
d2 = -0.437376
N(d1) = Cumulative standard normal dist. of d1
N(d1) =0.744499
N(d2) = Cumulative standard normal dist. of d2
N(d2) =0.330919
Value of call= 21.7*0.744499-0.330919*20.8*e^(-0.026*3)
Value of call= 9.79