What is the value of the american put given the parameters

Reference no: EM133583641

Assignment

Question I. When there are no dividends, the early exercise of an American put depends on a tradeoff between insurance value (which comes from volatility) and time value (a function of interest rates). Thus, for example, for a given level of volatility, early exercise of the put becomes more likely if interest rates are higher. This question provides a numerical illustration Consider a two-period binomial model with u = 1.10 and d = 0.90. Suppose the initial stock price is 100, and we are looking to price a two-period American put option with a strike of K = 95.

1. First, consider a "low" interest rate of R = 1.02. Show that early exercise of the American put is never optimal in this case.

2. Now consider a "high" interest rate of R = 1.05. Show that it now becomes optimal to exercise the put early in some circumstances. What is the early exercise premium in this case?

Question II. Consider a two-period example with S = 100, u = 1.10, d = 0.90, R = 1.02, and a dividend of $5 after one period. Is early exercise of a call optimal given these parameters?

Question III. We repeat the previous question with higher volatility and interest rates and with lower dividends. Consider a two-period binomial tree with the following parameters: S = 100, u = 1.20, d = 0.80, and R = 1.10. Suppose also that a dividend of $2 is expected after one period.

1. Compute the risk-neutral probability in this world.

2. Find the tree of prices of an American call option with a strike of 100 expiring in two periods.

3. What is the early-exercise premium?

Question IV. The payment of a dividend on the underlying stock increases the value of a put option since it "lowers" the stock price distribution at maturity. This question provides a numerical illustration.

Let a two-period binomial tree be given with the following parameters: S = 100, u = 1.10, d = 0.90, and R = 1.05. Consider a two-period American put option with a strike of 90. Note that this put is quite deep out-of-the-money at inception.

1. What is the value of the American put given these parameters?

2. Now suppose a dividend of $4 is paid at the end of the first period. What is the new price of the put?

Reference no: EM133583641

Questions Cloud

Has the potential to not only save significant costs : Has the potential to not only save significant costs but also enhance its market reputation, customer trust, and shareholder value.

Techniques for each step of effective delegation : Describe the principles and techniques for each step of effective delegation. Gantt charts are one of the most commonly used project management tools.

Essay on counselling theory and case study application : Essay on Counselling Theory and Case Study Application - Identification of the historical origins and evolution of BOTH of your chosen theories

Explain the codes of practice used in home and community : Explain the codes of practice used in home and community services and how they impact the provision of service What are six (6) ways support workers can set

What is the value of the american put given the parameters : What is the value of the American put given the parameters? Now suppose a dividend of $4 is paid at the end of first period. What is the new price of the put?

Describe the report sections you will include in your course : Describe the report sections you will include in your course project to describe your CDC healthcare improvement initiative?

Which risk of drinking alcohol while taking ibuprofen : which risk of drinking alcohol while taking ibuprofen? Increased risk of nephrotoxic effects Decreasing ibuprofen's anti-inflammatory effect Increased risk

Explain two of the four reasons that family, community : Explain two of the four reasons that family, community, and religion are so influential in all cultures. What are stereotypes and how do people acquire them?

Characteristic of decentralized operations : Determine whether each of the following is a characteristic of decentralized operations. Many managers of a company making decisions for their division.

User Account

All Pages