1. Which of the following are always positively related to the price of a European call option on a stock?

I Strike Price

II Time to expiration

III Volatility

IV Risk free rate

V Amount of Dividends

1. I & III
2. IV & V
3. II and III
4. III and IV
5. All of the above

American style options can be valued using a binomial tree by doing which of the following:

1. Checking whether early exercise is optimal at all nodes where the option is in-the-money
2. Checking whether early exercise is optimal at the final nodes
3. Checking whether early exercise is optimal at the penultimate nodes and the final nodes
4. Increasing the number of time steps on the tree
5. None of the above

1. Volatility for purposes of pricing options, is typically measured as:
   1. The variance of the stock price on an annual basis
   2. The standard deviation of the stock price on the annual basis
   3. The standard deviation of the stock return on an annual basis
   4. The variance of the stock return on an annual basis
   5. The VIX
2. In the Black-Scholes-Merton option pricing formula N(d₁) denotes
   1. The area under a normal distribution from zero to d₁
   2. The are
   3. a under a normal distribution beyond d₁
   4. The area under a normal distribution up to d₁
   5. The area under the normal distribution between -d₁ and d₁
3. The VIX index measures
   1. Historical volatilities for options trading on the S&P 500 index
   2. Historical volatilities for stock options trading on CBOE
   3. Implied volatilities for options trading on the S&P 500 index
   4. Implied volatilities for stock options trading on CBOE
   5. A menthol-based petroleum jelly
4. Which of the following statements is incorrect?
   1. The initial margin is the money placed with the clearinghouse when the trade is initially executed
   2. To buy a futures contract, you must satisfy the initial margin requirement
   3. The maintenance margin is always smaller than the initial margin
   4. Futures margins are usually significantly lower than margins for stocks
   5. The maintenance margin is only required for sellers of futures contracts
5. To determine the fixed rate on a swap, you would
   1. Use put-call parity
   2. Price it as the issuance of a fixed rate bond and purchase of a floating rate bond or vice versa
   3. Use the same fixed rate as that of a zero coupon bond of equivalent maturity
   4. Use the continuously compounded rate for the shortest maturity bond
   5. None of the above
6. Find the net payment on an equity swap in which party A pays the return on a stock index and party B pays a fixed rate of 6 percent. The notional amount is $10 million. The stock index starts off at 1,000 and is at 1,055.15 at the end of the period. The interest payment is calculated based on 180 days in the period and 360 days in the year.
   1. party B pays $851,500
   2. party B pays $48,500
   3. party B pays $251,500
   4. party A pays $251,500
   5. part A pays $851, 500
7. You purchase one IBM put contract with strike price = $100 for a premium of $6 per option. The contract represents 100 put options, so the total premium is $600.00. What is the maximum profit that you could gain from this strategy?
   1. $10,000
   2. $10,600
   3. $9,400
   4. $9,000
   5. None of the above
8. Nowel Inc. stock is currently priced at $42. The present value of the strike price of a call option on this stock is $44. Probability one, as calculated by the Black Scholes option pricing model is .6541; probability 2 is .3722. The value of this option as calculated by Black-Scholes is
   1. -$2.00
   2. $11.10
   3. $2.00
   4. $10.71
   5. $2.71