Question

The common shares of Twitter, Inc. (TWTR) recently traded on the NYSE for $20.10 per share. You have employee stock options to purchase 1,000 TWTR shares for $18.4 per share. The options expire in three years. Assume that the annualized volatility of TWTR stock is 87.0 percent and that the interest rate is 3.3 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 61.6 percent? (Round option value per share to 2 decimal places.)

Answer 1

(a) This is a call option

(b)

S₀ = $20.10

K = $18.4

T = 3 years

$\sigma$ = 0.87

r = 0.033

Using Black-Scholes formula we have

d₁ = { ln(S₀/K) + (r + 0.5$\sigma$²)T } / ($\sigma$T^0.5) = { ln(20.10/18.4) + (0.033 + 0.5x0.87²)x3 } / (0.87x3^0.5) = 0.8778

d₂ = d₁ - $\sigma$ T^0.5 = 0.8778 - 0.87x3^0.5 = - 0.6291

$\therefore$$\Phi$(d₁) = $\Phi$ (0.8778) = 0.80997, where $\Phi$ () is the cumulative distribution function for standard normal distribution

$\Phi$(d₂) = $\Phi$ (-0.6291) = 0.26464

Hence price of the option = S_t$\Phi$(d₁) - Ke^-rT$\Phi$(d₂)= 20.10x0.80997 - 18.4xe^-0.033x3x0.26464 = $11.87

(c)

Similarly for

S₀ = $20.10

K = $18.4

T = 0.5 years

$\sigma$ = 0.87

r = 0.033

we have option price = $5.69

(d)

Similarly for

S₀ = $20.10

K = $18.4

T = 3 years

$\sigma$ = 0.616

r = 0.033

Option price = $9.30