Question 5 The current S&P100 index level is $1863.59. You want to buy a four-month American put option on the index with an exercise price of $1850.00. The riskless interest rate is 2% and the index pays dividends of 1.5% (both of these rates are annualized and continuously compounded). You estimate that the annualized index volatility rate over the next four months is 18%. Value the option using a seven-step binomial tree. (a) What is the stock price in the upper righthand comer of your binomial tree (i.e., if there are seven con- secutive upsteps)? What is the stock price in the bottom righthand corner (seven consecutive down- steps)? What are the corresponding option prices? (Please report your answers to two decimal places.) (b) What are the prices one time step before the bottom righthand corner of your binomial tree, i.e., after six consecutive downsteps? (Please report your answers to two decimal places.) (c) What is the current value of the option? (Please report your answer to two decimal places.) (d) Suppose you're a market maker who sells this put option to a customer. How would you synthetically create the option to offset your risk? Be sure to identify the securities traded, whether you buy or sell these securities, and the quantities you should trade. Would you hold this portfolio to expiration? | Question 5 The current S&P100 index level is $1863.59. You want to buy a four-month American put option on the index with an exercise price of $1850.00. The riskless interest rate is 2% and the index pays dividends of 1.5% (both of these rates are annualized and continuously compounded). You estimate that the annualized index volatility rate over the next four months is 18%. Value the option using a seven-step binomial tree. (a) What is the stock price in the upper righthand comer of your binomial tree (i.e., if there are seven con- secutive upsteps)? What is the stock price in the bottom righthand corner (seven consecutive down- steps)? What are the corresponding option prices? (Please report your answers to two decimal places.) (b) What are the prices one time step before the bottom righthand corner of your binomial tree, i.e., after six consecutive downsteps? (Please report your answers to two decimal places.) (c) What is the current value of the option? (Please report your answer to two decimal places.) (d) Suppose you're a market maker who sells this put option to a customer. How would you synthetically create the option to offset your risk? Be sure to identify the securities traded, whether you buy or sell these securities, and the quantities you should trade. Would you hold this portfolio to expiration? |