Please answer the following questions in detail, provide examples whenever applicable, provide in-text citations.

1.Discuss the risks and payoffs of the following positions, accompanied by payoff graphs.

1.Buy stock and a put option on the stock.

2.Buy a stock.

3.Buy a call.

4.Buy stock and sell a call option on the stock (covered call).

5.Buy a bond.

6.Buy stock, buy a put, and sell a call.

7.Sell a put (naked put).

2. What is put-call parity and why does it hold? Could you apply the parity formula to a call and put options with different exercise prices?

3. Over the coming year, Ragwort's stock price might drop from $100 to $50 or it might rise to $200. The one-year interest rate is 10%.

1.What is the delta of a one-year call option on Ragwort stock with an exercise price of $100?

2.Use the replicating-portfolio method to value this call.

3.In a risk-neutral world, what is the probability that Ragwort stock will rise in price?

4.Use the risk-neutral method to check your valuation of the Ragwort option.

5.If someone told you that in reality there is a 60% chance that Ragwort's stock price will rise to $200, would you change your view about the value of the option? Explain.