Question

1. Taggart Transcontinental’s stock has a volatility of 25% and a current stock price of $40 per share. Taggart pays no dividends. The risk-free interest rate is 4%.

(a). Calculate the Black-Scholes value of a one-year, at-the-money call option on Taggart stock.

The value of a one-year, at-the-money call option on Taggart stock is _______$ (round to two decimal places)

(b). Calculate the Black-Scholes value of a one-year, at-the-money put option on Taggart stock.

The value of a one-year, at-the-money put option on Taggart stock is_______ $ (round to two decimal places)

(c). Calculate the Black-Scholes value of a one-year call option on Taggart stock with a strike price of $50.

The value of a one-year call option on Taggart stock with a strike price of $50 is ________$ (round to two decimal places)

(d). Consider a one-year, at-the-money call option on Taggart stock. Compute the effect on the price of this call option of an increase in the risk-free rate from 4% to 6%.

The effect on the price of the call option is _________$ plug in increase or decrease __________. (round to two decimal places)

(e). Consider a one-year, at-the-money call option on Taggart stock. Compute the effect on the price of this call option of an increase in the volatility from 25% to 40%.

The effect on the price of the call option is _______$ plug in increase or decrease_______ . (round to two decimal places)

(f). Calculate the Black-Scholes Δ of a one-year, at-the-money call option on Taggart stock.

The Black-Scholes Δ of a one-year, at-the-money call option is __________ (round to four decimal places)

2. The current price of KD Industries stock is $20. In the next year the stock price will either go up by 20% or go down by 20%. KD pays no dividends. The one year risk-free rate is 4.0% and will remain constant.

(a). Using the binomial pricing model, calculate the price of a one-year call option on KD stock with a strike price of $20.

The price for a one-year call option on KD stock is_______ $ (round to two decimal places)

(b). Using the binomial pricing model, calculate the price of a one-year put option on KD stock with a strike price of $20.

The price for a one-year put option on KD stock is_______ $ (round to two decimal places)

Answer 1

S: current stock price

K: Strike price

r: risk free rate

s: volatility

t: time to maturity

c: price of call option

p: price of put option

exp: Natural exponential e

N(d1) = normsdist(d1) & N(d2) = normsdist(d2).......to calculate from excel

(a) At the money option means (S = K)

S = 40; K = 40; r = 4%; s = 25% ; t = 1 year

= 0.07125/0.25 = 0.285

d2 = d1 - s* t^0.5 = 0.285 - 0.25*1^0.5 = 0.285 - 0.25 = 0.035

N(d1) = 0.612 & N(d2) = 0.514

c = 40*0.612 - 40*exp^(-0.04*1)*0.514 = 24.48 -19.754 = 4.726 = 4.73

(b) Put call parity

c + K*exp^(-r*t) = p + S

4.73 + 40*exp^(-0.04*1) = P + 40

43.162 = p + 40

or p = 43.162 - 40 = 3.162

(c)  S = 40; K = 50; r = 4%; s = 25% ; t = 1 year

= (-0.223 + 0.07125)/0.25 = -0.15175

d2 = d1 - s* t^0.5 = -0.15175 - 0.25*1^0.5 = -0.15175 - 0.25 = -0.40175

N(d1) = 0.44 & N(d2) = 0.343

c = 40*0.44 - 50*exp^(-0.04*1)*0.343 = 17.6 - 16.478 = 1.122 = 1.12

(d) S = 40; K = 40; r = 6%; s = 25% ; t = 1 year

= (0.09125)/0.25 = 0.365

d2 = d1 - s* t^0.5 = 0.365 - 0.25*1^0.5 = 0.365 - 0.25 = 0.115

N(d1) = 0.642 & N(d2) = 0.546

c = 40*0.642 - 40*exp^(-0.06*1)*0.546 = 25.68 - 20.568 = 5.112 = 5.11

Value of call option increases from 4.73 to 5.11