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# Stock Prices Calculations for Non-Dividends

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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.

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