Part 1 ( 2 pages ) Please answer the following questions in detail, provide examples whenever applicable, provide in-text


Part 1 ( 2 pages )

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.

  • 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).

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

  1. Over the coming year, Ragworts 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 Ragworts stock price will rise to $200, would you change your view about the value of the option? Explain. 

Part 2 ( 2 pages ) see the attached file 

You have an option to purchase all of the assets of the Overland Railroad for $2.5 billion. The option expires in nine months. You estimate Overlands current (month 0) present value (PV) as $2.7 billion. Overland generates after-tax free cash flow (FCF) of $50 million at the end of each quarter (i.e., at the end of each three-month period). If you exercise your option at the start of the quarter, that quarters cash flow is paid out to you. If you do not exercise, the cash flow goes to Overlands current owners. 

In each quarter, Overlands PV either increases by 10% or decreases by 9.09%. This PV includes the quarterly FCF of $50 million. After the $50 million is paid out, PV drops by $50 million. Thus, the binomial tree for the first quarter is (figures in millions):

The risk-free interest rate is 2% per quarter.

  1. Build a binomial tree for Overland, with one up or down change for each three-month period (three steps to cover your nine-month option). 

  2. Suppose you can only exercise your option now, or after nine months (not at month 3 or 6). Would you exercise now? 

  3. Suppose you can exercise now, or at month 3, 6, or 9. What is your option worth today? Should you exercise today, or wait?

Please explain your answer in detail and provide in-text citations.


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