1. (a) Calculate the Black-Scholes prices of the European call and
put options with six-month maturity if the current stock
price is $20 and grows with average rate of m ¼ 10%, vola-
tility is 20%, and risk-free interest rate is 5%. The strike price
is: (1) $18; (2) $22.
(b) How will the results above change if m ¼ 5%?
2. Is there an arbitrage opportunity with the following assets: the
price of the XYZ stock with no dividends is $100; the European
put options at $98 with six-month maturity are sold for $3.50;
the European call options at $98 with the same maturity are sold
for $8; T-bills with the same maturity are sold for $98. Hint:
Check the put-call parity.
**3. Compare the Ito’s and Stratonovich’s approaches for derivation
of the Black-Scholes equation (consult ).
Option Pricing 109