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What is a lower bound for the price of a 4-month call option on a non-dividend

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1. What is a lower bound for the price of a 4-month call option on a non-dividend -paying stock when the stock price is $43.77, the strike price is $36, and the risk-free interest rate is 5% per annum?;2. If the underlying pays no dividend, then the early exercise payoff of an American call option is always smaller than the remaining value of the option.;True;False;3. Currently, a stock price is $53. Over each of the next 2 6-month periods it is expected to go up by 12% or down by 10%. The risk-free rate is 5% per annum with continuous compounding. What is the value of a 1-year European put option with a strike price of $50?;4. One should use straddle, if he thinks there will be a significant stock price move in either direction.;True;False;5. A call with a strike price of $70 costs $7.66. A put with the same strike price and expiration date costs $3.68. If you create a straddle, what is the initial cash flow?;6. Suppose you are creating a butterfly spread using 3 call options with different strike prices. Currently, the call price with strike price of $40 is $20.22, the call with strike price of $50 is $11.29, and the call with strike price of $60 is $5.55. What is the initial cash flow of the butterfly spread strategy?;7. Calculate the price of a 4-month European call option on a dividend-paying stock with a strike price of $30 when the current stock price is $32, the risk-free rate is 6% per annum and the volatility is 40% per annum. A dividend of $1.00 is expected in 2 months. Use Black-Scholes formula.;$3.05;$3.65;$4.32;$5.02;8. Suppose that put options on a stock with strike prices $45 and $55 cost $5 and $8, respectively. Use these options to create a bear spread. At what stock price at maturity will you break even? In other words, at what stock price, will you make $0 profit?;9. Which of the following does not affect the Black-Scholes option prices for a non dividend paying stock?;current stock price;strike price;expected return of stock;volatility of stock;risk-free interest rate;10. A call option expiring in 40 trading days has a market price of $7. The current stock price is $55, the strike price is $50, and the risk-free rate is 3% per annum. Calculate the implied volatility.;33.23%;34.57%;42.62%;46.04%;11. Suppose the current stock price is $50. At the end of 6 months it will be either $58 or $43. The risk-free interest rate is 3% per annum. What is the risk-neutral probability that the stock price will increase in 6 months? Report in percentage such as 55.55%.;12. Higher strike price increases the value of put options.;True;False;13. The price of an American call on a non-dividend-paying stock is $4.25. The stock price is $41.42, 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?;14. Suppose your portfolio mirrors S&P500 index and is valued currently at $1,000,000. The S&P 500 index is currently at 2,000. What action is needed to provide protection against the value of the portfolio falling below $900,000 in 6 months?;Buy 5 6-month S&P500 put option contracts with strike price of 1800.;Buy 5 6-month S&P500 put option contracts with strike price of 1900.;Buy 10 6-month S&P500 put option contracts with strike price of 1800.;Buy 10 6-month S&P500 put option contracts with strike price of 1900.;15. Currently, a stock price is $80. It is known that at the end of 4 months it will be either $70 or $90. The risk-free rate is 6% per annum with continuous compounding. What is the value of a 4-month European put option with a strike price of $80?;16. Currently the index is standing at 1,097. The risk-free rate is 4% per annum and the dividend yield is 1% per annum. A 6-month European put option on the index with a strike price of 1000 is trading at $32.04. What is the value of a 6-month European call option on the index with the same strike price?;17. The price of a non-dividend paying stock is $20.93 and the price of a 3-month European call option on the stock with a strike price of $20 is $7.8. The risk-free rate is 5% per annum. What is the price of a 3-month European put option with a strike price of $20?;Additional Requirements;Level of Detail: Show all work

 

Paper#21123 | Written in 18-Jul-2015

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