Problem 2. The Standard \& Poor's 100 Index is a capitalization-weighted index of 100 stocks from a broad range of industries. The component stocks are weighted according to the total market value of their outstanding shares. The impact of a component's price change is proportional to the issue's total market value, which is the share price times the number of shares outstanding. The base value for the S\&P 100 Index is adjusted to reflect changes in capitalization resulting from mergers, acquisitions, stock rights, substitutions, etc. The symbol for the underlying index is OEX. The exercise of S\&P 100 options are American style. That is, the options generally may be exercised on any business day up to and including on the expiration date. The expiration day is the third Friday of the expiration month. The exercise-settlement value, OEX, is calculated using the last (closing) reported sales price in the primary market of each component stock on the expiration date or on the day the exercise notice is properly submitted if exercised before expiration. The exercise-settlement amount is equal to the difference between the exercise-settlement value, OEX, and the exercise price of the option, multiplied by $100. Exercise will result in delivery of cash on the business day following the day the exercise notice is properly submitted. Consider an eight-month call option on the S\&P 100 index with strike price 1150 . The current S\&P index is 1054.50 , and its dividend yield is 2%. The interest is 1% per annum. The volatility of the index is 20% per annum. (In your solution, report index and option values with two digits after decimal points but report u,d, and q with four decimal numbers.) (a) Create an eight-step binomial model for the S\&P 100 index on a spreadsheet. Display the result of your binomial model. (b) On each node of your binomial model, what is the risk-neutral probability for the index to go down in the next step? (c) Suppose you have five contracts of S\&P 100 index options, what is the value of your contracts (round to a dollar)? (d) Is it optimal to exercised these call option contracts early on some nodes of the price tree? Does your answer conflict with the rule of no early exercise of American call options? Problem 2. The Standard \& Poor's 100 Index is a capitalization-weighted index of 100 stocks from a broad range of industries. The component stocks are weighted according to the total market value of their outstanding shares. The impact of a component's price change is proportional to the issue's total market value, which is the share price times the number of shares outstanding. The base value for the S\&P 100 Index is adjusted to reflect changes in capitalization resulting from mergers, acquisitions, stock rights, substitutions, etc. The symbol for the underlying index is OEX. The exercise of S\&P 100 options are American style. That is, the options generally may be exercised on any business day up to and including on the expiration date. The expiration day is the third Friday of the expiration month. The exercise-settlement value, OEX, is calculated using the last (closing) reported sales price in the primary market of each component stock on the expiration date or on the day the exercise notice is properly submitted if exercised before expiration. The exercise-settlement amount is equal to the difference between the exercise-settlement value, OEX, and the exercise price of the option, multiplied by $100. Exercise will result in delivery of cash on the business day following the day the exercise notice is properly submitted. Consider an eight-month call option on the S\&P 100 index with strike price 1150 . The current S\&P index is 1054.50 , and its dividend yield is 2%. The interest is 1% per annum. The volatility of the index is 20% per annum. (In your solution, report index and option values with two digits after decimal points but report u,d, and q with four decimal numbers.) (a) Create an eight-step binomial model for the S\&P 100 index on a spreadsheet. Display the result of your binomial model. (b) On each node of your binomial model, what is the risk-neutral probability for the index to go down in the next step? (c) Suppose you have five contracts of S\&P 100 index options, what is the value of your contracts (round to a dollar)? (d) Is it optimal to exercised these call option contracts early on some nodes of the price tree? Does your answer conflict with the rule of no early exercise of American call options