a$)$ You are given the following information: Stock ABC price is $$45,$ monthly interest rate is $1\%,$ and a put option on ABC with maturity in $4$ months is currently priced at $$5.$ Strike price of this option is $$50.$ Infer what should be the no$-$arbitrage price of a call option with the same maturity and strike price of the put option. $(3$ marks$)$b$)$ When are cash flows in forward contracts exchanged? Draw a diagram of the payoff of a long and a short position in a forward contract. $(5$ marks$)$

c$)$ Explain what a speculation activity is and how one would use a stock or a single option $($put or call$)$ to speculate $($give the simplest example$).(5$ marks$)$

d$)$ Consider stock XYM$.$ Its price is $$100,$ the monthly interest rate is $0\mathrm{.}5\%,$ and a put option on XYM with maturity in $5$ months is currently priced at $$5.$ Strike price of this option is $$90.$ The price of a call option with the same maturity and strike price of the put option is currently priced at $$20.$ Is this an arbitrage opportunity? If yes, explain how to take advantage of it and provide a cash flow diagram showing your strategy. $(7$ marks$)$