# On March 2, a Treasury bill expiring on April 20 had a bid discount of 5.80

Question

On March 2, a Treasury bill expiring on April 20 had a bid discount of 5.80, and an ask discount of 5.86.What is the best estimate of the risk-free rate as given in the text?

The stock price was 113.25. The risk-free rates were 7.30 percent(November), 7.50 percent (December) and 7.62 percent (January). Thetimes to expiration were 0.0384 (November), 0.1342 (December), and0.211 (January). Assume no dividends unless indicated.

Puts

CallsStrike

Nov

Dec

Jan

Nov

Dec

Jan

105

8.4

10

11.5

5.3

1.3

2

110

4.4

7.1

8.3

0.9

2.5

3.8

115

1.5

3.9

5.3

2.8

4.8

4.8

What is the intrinsic value of the December 115 put?Answer: 1.75

Consider a binomial world in which the current stock price of 80 can either go up by 10percent or down by 8 percent. The risk-free rate is 4 percent. Assume a one-period world.Answer questions 12 through 15 about a call with an exercise price of 80.What is the theoretical value of the call?Answer: 5.15

A stock priced at 50 can go up or down by 10 percent over two periods. The risk-free rate is 4 percent. Whichof the following is the correct price of an American put with an exercise price of 55?

The following information is given about options on the stock of a certain companyS0 = 23X = 20rc = 0.09T = 0.52= 0.15What value does the Black-Scholes-Merton model predict for the call? (Due to differences in rounding yourcalculations may be slightly different. “none of the above” should be selected only if your answer is differentby more than 10 cents.)

The following information is given about options on the stock of a certain companyS0 = 23X = 20rc = 0.09T = 0.52 = 0.15If we now assume that the stock pays a dividend at a known constant rate of 3.5 percent, what stock priceshould we use in the model? (Due to differences in rounding your calculations may be slightly different.“none of the above” should be selected only if your answer is different by more than 10 cents.)

Consider a stock priced at $30 with a standard deviation of 0.3. The risk-free rate is 0.05. There are put and call optionsavailable at exercise prices of 30 and a time to expiration of six months. The calls are priced at $2.89 and the puts cost$2.15. There are no dividends on the stock and the options are European. Assume that all transactions consist of 100shares or one contract (100 options).What is the breakeven stock price at expiration $27?

The following prices are available for call and put options on a stock priced at $50. The risk-free rate is 6percent and the volatility is 0.35. The March options have 90 days remaining and the June options have 180days remaining. The Black-Scholes model was used to obtain the prices.

Strike455055

CallsMarchJune6.848.413.825.581.893.54

PutsMarchJune1.182.093.084.136.086.93

Assume that each transaction consists of one contract (for 100 shares) unless otherwise indicated.What is the profit if the stock price at expiration is $47?

The following prices are available for call and put options on a stock priced at $50. The risk-free rate is 6percent and the volatility is 0.35. The March options have 90 days remaining and the June options have 180days remaining. The Black-Scholes model was used to obtain the prices.

Strike455055

CallsMarchJune6.848.413.825.581.893.54

PutsMarchJune1.182.093.084.136.086.93

Assume that each transaction consists of one contract (for 100 shares) unless otherwise indicated.What are the two breakeven stock prices at expiration using the June 50 options.

A futures contract covers 5000 pounds with a minimum price change of $0.01 is sold for $31.60 per pound. If theinitial margin is $2,525 and the maintenance margin is $1,000, at what price would there be a margin call?

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