A stock price is currently $50. It is know that at the end of 2 months it will be either $48 or $53. The arbitrage-free price of a 2 month European call on this stock (with a strike of $49) is $1.92.
a) An investor wants to build a riskless portfolio of shares and one option. The number of shares he should buy is called the B of the option. What is the B of this call?
b) What is the annual volatility?
c) Find the value of the riskless portfolio at t = 0 and at expiration
d) Find the annual risk-free rate
e) If the call price is $1.60, there is arbitrage. Find the arbitrage profit, and use the reverse cashflow approach to describe how to obtain it.
f) In the previous problem e), if the call price is $1.75, there is arbitrage. Find the arbitrage profit, and describe how to obtain it.