Question

The common shares of Twitter, Inc. (TWTR) recently traded on the NYSE for $19.70 per share. You have employee stock options to purchase 1,000 TWTR shares for $17.8 per share. The options expire in three years. Assume that the annualized volatility of TWTR stock is 86.6 percent and that the interest rate is 3.1 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 your answer to nearest whole number.)

The common shares of Twitter, Inc. (TWTR) recently traded on the NYSE for $19.70 per share. You have employee stock options to purchase 1,000 TWTR shares for $17.8 per share. The options expire in three years. Assume that the annualized volatility of TWTR stock is 86.6 percent and that the interest rate is 3.1 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 your answer to nearest whole number.)

Value of your TWTR options:

c. What is the estimated value of the options if their maturity is six months instead of three years? (Round your answer to nearest whole number.)

Value of the options

d. What is the estimated value of the options if their maturity is three years, but TWTR’s volatility is 61.2 percent? (Round your answer to nearest whole number.)

Value of the options

Answer 1

(a) This is a call option

(b)

Common Share Price per Share, S₀ = $20.10

Share Price per Share, K = $18.4

Time, T = 3 years

Annualized Volatility Stock per Share, = 0.87

Rate of interest, r = 0.033

Applying Black-Scholes formula,

d₁ = { ln(S₀/K) + (r + 0.5²)T } / (T^0.5) = { ln(20.10/18.4) + (0.033 + 0.5x0.87²)x3 } / (0.87x3^0.5) = 0.8778

d₂ = d₁ - T^0.5 = 0.8778 - 0.87x3^0.5 = - 0.6291

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

(d₂) = (-0.6291) = 0.26464

Hence, Price of the option = S_t(d₁) - Ke^-rT(d₂)

= 20.10x0.80997 - 18.4xe^-0.033x3x0.26464

= $11.87

(c)

Common Share Price per Share, S₀ = $20.10

Share Price per Share, K = $18.4

Time, T = 0.5 years

Annualized Volatility Stock per Share, = 0.87

Rate of interest, r = 0.033

Option price = $5.69

(d)

Common Share Price per Share, S₀ = $20.10

Share Price per Share, K = $18.4

Time, T = 3 years

Annualized Volatility Stock per Share, = 0.616

Rate of interest, r = 0.033

Option price = $9.30