Question $6(10$ marks$)$

Stock A is selling at $$65$ with a volatility of $30\%.$ The beta of the stock is $2\mathrm{.}15.$ The call

option with exercise price of $$60$ has a premium of $$7\mathrm{.}27,$ and the put option with exercise

price of $$60$ costs $$1\mathrm{.}60.$ All options considered have a maturity of $3$ months. The risk$-$free

rate is $5\%.$

a$)$ Devise a zero$-$net$-$investment arbitrage strategy to exploit the mispricing. $(5$ marks$)$

b$)$ Suppose there is another put option with strike price $$62$ sells for $$1\mathrm{.}60.$ Devise a

zero$-$net$-$investment arbitrage strategy to exploit the mispricing between the two put

options. Assume that you hold the put options position until expiration, draw the

profit diagram at expiration for your position? $(5$ marks$)$