# Derivatives Study Guide Essay

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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 cash-settled 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 counter-party 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 no-arbitrage 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 0.

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 non-dividend 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 6-month 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 non-directional 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 non-dividend 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: No-arbitrage price of Put = C + Ke-r×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 no-arbitrage 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 55-strike put and buying the 50-strike 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 put-call parity using zero for put price:

Put price cannot

• be more than the strike price

• be less than price implied by put-call parity using zero for call price: