1. The price of an American call on a non-dividend-paying stock is $4.67. The stock price is $41.26, strike price is $39, and the expiration date is in 3 months. The risk-free rate is 6%. What is the upper bound for the price of an American put on the same stock with the same strike price and expiration date?
2. Calculate the price of a 3-month European put option on a dividend-paying stock with a strike price of $30 when the current stock price is $30, the risk-free rate is 15% per annum and the volatility is 40% per annum. A dividend of $1.00 is expected in 2 months. Use Black-Scholes formula.
3. Suppose you are creating a butterfly spread using 3 put options with different strike prices. Currently, the put price with strike price of $40 is $5.46, the put with strike price of $50 is $11.74, and the put with strike price of $60 is $20.42. What is the initial cash flow?
4. Currently the index is standing at 1,054. The risk-free rate is 10% per annum and the dividend yield is 2% per annum. A 9-month European put option on the index with a strike price of 1000 is worth $28.48. What is the value of a 9-month call option on the index with the same strike price?
5. Currently, a stock index is 947, the dividend yield on the index is 2% per annum, and the risk-free rate is 6% per annum. What is a lower bound for the price of a 6-month European put option on the index when the strike price is 1,028?
6. Consider an American call option on a dividend-paying stock where the stock price is $80, the strike price is $70, the risk-free rate is 10% per annum, the volatility is 35% per annum, and the time to maturity is 1 year. $3 dividends are expected to be paid in 5 months and 11 months. Value the option using binomial tree pricing with 12 steps.
The stock price calculations for non-dividends are examined.