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Consider a European call option on a non-dividend-paying stock where the stock price is $40, the strike price is $40, the risk-free rate is 4% per annum.
How high does the company's initial cash position have to be for the company to have a less than 5% chance of a negative cash position by the end of one year?
The expected stock price at the end of the next day. The standard deviation of the stock price at the end of the next day.
What are the probability distributions of the cash position after one month, six months, and one year?
What is the expected instantaneous return (including interest and capital gains) to the holder of the bond?
What is the probability that the stock price will be greater than 80 in two years? (Hint: ST > 80 when In ST > In 80.)
What is the probability distribution for the rate of return (with continuous compounding) earned over a two-year period?
The time to maturity is three months, and the risk-free interest rate is 5% per annum. What is the implied volatility?
What is an expression for the value of a derivative that pays off $100 if the price of a stock at time T is greater than K?
Calculate the mean and standard deviation of the distribution. Determine 95% confidence intervals.
What is the price of the option if it is a European call? What is the price of the option if it is an American call?
How high can the dividends be without the American option being worth more than the corresponding European option?
"Once we know how to value options on a stock paying a dividend yield, we know how to value options on stock indices, currencies, and futures."
What is a lower bound for the price of a six-month European call options on the index when the strike price is 290?
Derive upper and lower bounds for the price of an American put on the same stock with the same strike price and expiration date.
Why was the more source important to your understanding than other sources?
Consider an exchange-traded call option contract to buy 500 shares with a strike price of $40 and maturity in four months.
The option price is $3.50, the strike price is $60.00, and the stock price is $57.00. What is the initial margin requirement?
The price of the option is $3. What is the investor's minimum cash investment (a) if the stock price is $28 and (b) if it is $32?
The stock price is $47, the strike price is $50, and the risk-free interest rate is 6% per annum. What opportunities are there for an arbitrageur?
The term structure is flat, with all risk-free interest rate being 10% What is the price of a European put option that expires in six months.
Explain how a strangle can be created from these two options. What is the pattern of profits from the strangle?
How can the options be used to create (a) a bull spread and (b) a bear spread? Construct a table that shows the profit and payoff for both spreads.
Construct a table that shows the profit from a straddle. For what range of stock prices would the straddle lead to a loss?
Identify six different strategies the investor can follow and explain the differences among them.