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.