Derivatives Study Guide
Derivatives Study Guide
1. Both forward and futures contracts are traded on exchanges. : False 2. Futures contracts are standardized; forward contracts are not. : True 3. The S&P500 index futures contract is a physical delivery contract. The pork bellies futures contract is a cashsettled contract. : False
4. An American option can be exercised at any time during its life. : True 5. A put option will always be exercised at maturity if the strike price is greater than the underlying asset price. : True
6. The fact that the exchange is the counterparty to every futures contract issued is important because it eliminates interest rate risk. : False 7. Index arbitrage is a strategy which exploits differences between actual index futures prices and their noarbitrage values.: True
8. Who from the following list would be considered a speculator by entering into a futures or options contract on commodities?(b) Corn delivery truck driver 9. All of the positions listed will benefit from a price decline, except: (a) Short 10. A strategy consists of buying a market index product at $830 and longing a put on the index with a strike of $830. If the put premium is $18.00 and interest rates are 0.5% per month (monthly compounding), what is the profit or loss at expiration (in 6 months) if the market index is $810? (d) $43.76 loss
11. A strategy consists of longing a put on the market index with a strike of 830 and shorting a call option on the market index with a strike price of 830. The put premium is $18.00 and the call premium is $44.00. Interest rates are 0.5% per month (monthly compounding). Determine the net profit or loss if the index price at expiration is $830 (in 6 months). (c) $26.79 gain
12. Which of the following statements does NOT accurately reflect the relationship between securities and synthetic forward contracts? (c) Prepaid forward forward – zero coupon bond 13. (3points) If you expect a market downturn, one potential defensive strategy would be to b) sell stock index futures 14. Fisher Corp. common stock is priced at $36.50 per share. The company just paid its $0.50 quarterly dividend. Interest rates are 6.0% per year (continuously compounded). A $35.00 strike European call, maturing in 6 months, sells for $3.20. What is the price of a 6 month, $35.00 strike put option?(b) $1.64
15. Which of the following American options will NOT be exercised early? (d) Call on a nondividend paying stock 16. Call options with strikes of $30, $35, and $40 have option premiums of $2.00, $1.70, and $1.50, respectively. Using strike price convexity, which option premium, if any, is not possible?(d) All are possible
17. Compute for the following call option. The stock is selling for $23.50. The strike price is $25. The possible stock prices at the end of 6 months are $27.25 and $21.75.(a) 0.4091 18. (3points) A stock is selling for $53.20. Interest rates are 6.0% (continuously compounded) and the returns on the stock have a standard deviation of 24.0%. What is the forecasted up movement in the stock over a 6month interval?(a) $64.96
1. An investor simultaneously sells one September call option on the S&P 500 Index with an exercise price of 1400 and one September put option on the S&P 500 Index with an exercise price of 1400.
a. What is the name of this strategy?
Answer: This is a written straddle on the S&P500 index with a strike price of 1,400. b. Given these positions, explain the investor’s view of the value of the S&P index. Answer: The investor is taking a nondirectional view of the S&P500 index. The investor has sold equal number of put and call options. Thus, his or her view of volatility is symmetric. The investor believes will not be a lot of movement in the S&P500 index through September.
c. For what range of stock prices does the position lead to a profit? Answer: The size of the profit will depend on the premiums. The larger the premiums the larger the range of the profits. The profit range will equal: 1,400 – FV (call put premiums) Stock price 1400 FV(call put premiums) 2. The necessary condition for early exercise is that we prefer to receive something sooner rather than later. With a dividend paying call and a nondividend paying put, what do we receive?Answer: With the call and the put we receive the dividend on the stock and the interest on the strike, respectively.
3. Manchester United Corp. common stock is priced at $74.20 per share. The company just paid its $1.10 quarterly dividend. Interest rates are 6.0% (continuously compounded). A $70.00 strike European call, maturing in 6 months, sells for $6.50. How much arbitrage profit/loss is made by shorting the corresponding European put, which is priced at $2.50?Answer: Noarbitrage price of Put = C + Ker×T – (S0 – PV(D)) = 6.50 + 70 e(0.06/2) – (74.20 – 1.10 e(0.06/4) – 1.10 e(0.06/2)) = 2.38
P/L = 2.50 – 2.38 = 0.12 profit
4. Suppose European put prices are given by
What noarbitrage property is violated? What spread position would you use to effect arbitrage? Demonstrate that the spread position is an arbitrage. Answer: The difference in put premiums is greater than the difference in strike prices. We could engage in arbitrage by selling the 55strike put and buying the 50strike put, which is a bull spread.
5. (10 points) Let S=40, K=40, r=8% (continuously compounded), σ=30%, =0, T=0.5 years, and number of binomial periods=2. Compute the prices of American call and put options.
Payoff for
Long forward = Spot price at expiration – Forward price Short forward = Forward price – Spot price at expiration A call option gives the owner the right but not the obligation to buy the underlying asset at a predetermined price during a predetermined time period
• Strike (or exercise) price: the amount paid by the option buyer for the asset if he/she decides to exercise
• Exercise: the act of paying the strike price to buy the asset • Expiration: the date by which the option must be exercised or become worthless
• Exercise style: specifies when the option can be exercised
• Payoff = Max [0, spot price at expiration – strike price] • Profit = Payoff – future value of option premium
Payoff/profit of a purchased (i.e., long) putSynthetic security creation using parity
Option price boundaries
Call price cannot
• be negative
• exceed stock price
• be less than price implied by putcall parity using zero for put price:
Put price cannot
• be more than the strike price
• be less than price implied by putcall parity using zero for call price:
B

Subject: Stock,

University/College: University of Arkansas System

Type of paper: Thesis/Dissertation Chapter

Date: 11 November 2016

Words:

Pages:
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