Ragwort’s stock price

Please answer one of the following questions in detail, providing examples whenever applicable.

1. Discuss the risks and payoffs of the following positions, accompanied by payoff graphs.
   • Buy stock and a put option on the stock.
   • Buy a stock.
   • Buy a call.
   • Buy stock and sell a call option on the stock (covered call).
   • Buy a bond.
   • Buy stock, buy a put, and sell a call.
   • Sell a put (naked put).

-OR-

2. 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%.
   • What is the delta of a one-year call option on Ragwort stock with an exercise price of $100?
   • Use the replicating-portfolio method to value this call.
   • In a risk-neutral world, what is the probability that Ragwort stock will rise in price?
   • Use the risk-neutral method to check your valuation of the Ragwort option.
   • 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.