b$).$ Suppose that a put option written on the same stock with the same exercise price and expiry as the call option

above is currently trading at $$0\mathrm{.}30.$ Design an arbitrage strategy to exploit the violation of the put$-$call parity,

assuming that you could freely buy and short$-$sell the underlying stock, the risk$-$free bond yielding the risk$-$free

rate, the call option, and the put option.

c$).$ Suppose another call option written on the same stock with the same expiry but with an exercise price of $$35$ is

selling at $$0\mathrm{.}43.$ You are cautiously bullish that the underlying stock will remain at a price range between $$25$ and

$$35$ at the expiry, and constructed the bull spread with the $25$ call and the $35$ call options.

Explain what should be the net profit $($payoff net of cost$)$ on your bull spread, if the underlying stock price is $$31$ on

the expiration day.