What is the value of the american put given the parameters

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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

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