Question

Consider a European option on a non-dividend-paying stock when the stock price is $30, the exercise price is $29, continuously compounded risk-free interest rate is 5%, volatility is 25% per annum, and time to maturity is 4 months (assume 4 months equals 120 days).

a. Find values of Delta for the two options.

b. Using just delta, what should be the change in the price of the call option if the price of the underlying stock increases by $0.04?

d. Find values of Theta for the two options.

e. What is the effect of theta on a long call option?

Answer 1

Given,

S (Price of the underlying) = 30

K (Option strike price) = 29

r (Risk free Interest Rate) = 5%

(Volatility) = 25%

t (time to expiry/maturity) = 120 days

a) Delta (): N(d1)

   

i. Call Option = 0.6638

ii. Put Option = -0.3362

b). Change in Call Option Price = $0.04*0.6638 = 0.027

      The price of the call option should increase by ~$0.03.

c). Theta

   i. Call Option = -0.0089

ii. Put Option = -0.0050

d) The Theta (or time decay factor) is the rate at which an option loses value as time passes. Theta is indicated in points lost per day when all other conditions remain the same. A long option will always have a negative theta meaning rest of the factors remaining constant, the option buyer will lose money on a day by day basis.