The following information is given about options on the stock of a certain company:
S0 = 23
X = 20
rc = 0.09
T = 0.5
theta^2 = 0.15
Answer the questions below (you may find the BSM spread sheets useful):
a. What value does the Black-Scholes-Merton model predict for the call?
b. To construct a riskless hedge, what is the number of calls per 100 shares purchased?(assume each call option is written on one share of stocks)
c. What does the call's rho measure? If the continuous compounded risk-free rate falls to 0.05, what is the estimated call option price?
d. What does the call’s vega measure? If the volatility goes to 0.62 , what is the estimated call option price?
e. What does the call’s theta measure? What is the estimated call option price in five days?
f. If the actual call price is 6.79, what is the implied standard deviation?