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##### MFE Financial Derivatives Homework 5 and 6

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Question;MFE Financial Derivatives Homework 5 (Chapters 9 and 10)Multiple ChoiceIdentify the choice that best completes the statement or answers the question.1 Which of the following would have the same value at t = 0 as an at-the-money call option on a forward contractpriced at FT (the forward price at time = 0)?A) A put option on the forward at the same exercise price.B) A put option, long the underlying asset, and short a risk-free bond that pays X-F T atoption expiration.C) A put option, long the underlying asset, and short a risk-free bond that pays X at optionexpiration.D) A put option, short the underlying asset, and long a risk-free bond that pays X at optionexpiration.2 Referring to put-call parity, which one of the following alternatives would allow you to create a synthetic stockposition?A) Sell a European call option, buy a European put option, short the present value of theexercise price worth of a riskless pure-discount bond.B) Buy a European call option, buy a European put option, invest the present value of theexercise price in a riskless pure-discount bond.C) Buy a European call option, short a European put option, invest the present value of theexercise price in a riskless pure-discount bond.D) Buy a European call option, buy a European put option, short the present value of theexercise price in a riskless pure-discount bond.3 Which of the following options will NOT be exercised early?A) Put on a dividend paying stockC) Put on a non-dividend paying stockB) Call on a dividend paying stockD) Call on a non-dividend paying stock4 Which of the following statements regarding an option prior to expiration is most accurate? The maximum value ofa(n):A) European call is greater than the maximum value of an American call.B) American put is equal to the maximum value of a European put.C) American call is equal to the maximum value of a European call.D) European put is greater than the maximum value of an American put.5 Compared to European put options on an asset with no cash flows, an American put option:A) will have the same minimum value.C) will have a lower minimum value.B) will have a higher minimum value.D) will have a lower maximum value.6 A put option with an exercise price of 59 on a non-dividend-paying stock expires in 3 months. The underlyingstock is trading at 53 and the risk-free rate is 5%. The minimum value of an American-style put and of aEuropean-style put are closest to:A) American put $5.28European put $6.00B) American put $6.00European put $6.00C) American put $6.00European put $5.28D) American put $5.28European put $5.287 Consider a call option expiring in 60 days on a non-dividend-paying stock trading at 53 when the risk-free rate is5%. The lower bound for a call option with an exercise price of 50 is:A) $0.C) $3.40.B) $3.00.D) $4.22.18 The lower bound on European put option prices can be adjusted for cash flows of the underlying asset by:A) subtracting the present value of the expected dividend payments from the exercise price.B) adding the present value of the expected dividend payments to the exercise price.C) subtracting the present value of the expected dividend payments from the current assetprice.D) adding the present value of the expected dividend payments from the current asset price.9 A stock is priced at 40 and the periodic risk-free rate of interest is 8%. The value of a two-period European calloption with a strike price of 37 on a share of stock using a binomial model with an up factor of 1.20 and a downfactor of 0.833 is closest to:A) $9.13.C) $3.57.B) $9.25.D) $6.82.10 A stock is priced at 38 and the periodic risk-free rate of interest is 6%. What is the value of a two-period Europeanput option with a strike price of 35 on a share of stock using a binomial model with an up factor of 1.15 and adown factor of 1/1.15, assuming a risk-neutral probability of 68%?A) $0.64.C) $0.57.B) $2.58.D) $1.90.11 Regarding deep in-the-money options on forwards, it is:A) sometimes worthwhile to exercise calls early but not puts.B) sometimes worthwhile to exercise both calls and puts early.C) never worthwhile to exercise puts or calls early.D) sometimes worthwhile to exercise puts early but not calls.*************************************************************************MFE Financial Derivatives Homework 6 (Chapter 12)Multiple ChoiceIdentify the choice that best completes the statement or answers the question.1 Which of the following is least likely one of the assumptions of the Black-Scholes-Merton option pricing23456model?A) There are no cash flows on the underlying asset.B) Changes in volatility are known and predictable.C) The risk-free rate of interest is known and does not change over the term of theoption.D) The returns of the underlying asset follow a normal distribution.The value of a put option will be higher if, all else equal, the:A) exercise price is lower.B) underlying asset has less volatility.C) underlying asset has positive cash flows.D) risk-free interest rate is higher.The price of a June call option with an exercise price of $50 falls by $0.50 when the underlying stockprice falls by $2.00. The delta of a June put option with an exercise price of $50 is closest to:A) 0.25.C) 0.25.B) 0.75.D) 0.75.Gamma is the greatest when an option:A) is at the money.C) is deep out of the money.B) is deep in the money.D) is far from expiration.If we use four of the inputs into the Black-Scholes-Merton option-pricing model and solve for the assetprice volatility that will make the model price equal to the market price of the option, we have found the:A) option volatility.C) historical volatility.B) implied volatility.D) theoretical volatility.Robert Walter is a recently retired executive from Cardinal Industries. Over the years he has accumulated$10 million worth of Cardinal stock, which is currently traded at $50/share, and another $2 million in acash savings account. Walter would like to consider neutralizing his Cardinal equity position fromchanges in the stock price of Cardinal. Using the information in the Table below, how many standardCardinal European options would have to be bought/sold in order to create a delta neutral portfolio?Cardinal (at-the-money) Option InformationPremiumEuropean callEuropean putAmerican callAmerican putdelta$6.31$4.83$6.28$4.960.5977-0.40230.5973-0.4258A) Buy 497,141 put options.B) Sell 497,141 put options.C) Sell 119,540 call options.D) Buy 370,300 call options.1Financial Derivatives HW67 Frank Inslee, a trader for Seattle Neutral, an option dealer, set up a delta hedged portfolio for a writtencall position one day ago (on day 0). Some details about the delta hedged portfolio are given in the tablebelow. The option is a 60-day European call with a strike price at $45 on AMP, a financial stock, onwhich Seattle Neutral has written 500 calls when its price was $42/share. The risk-free interest rate is4%.Days12Call PremiumCall Delta0.891.310.381710.49180AMP ClosingPrice43.5044.50Bond Balance-3,263?Whats the dollar difference between the actual value of the delta hedged portfolio value beforeadjustment for new delta value and its projected on Day 2?A) -32.C) -20.B) 65.D) 44.8 In delta-hedging a call position, which of the following pairs of conditions would lead to the gammaeffect being the most important? The call is:A) at-the-money and near expiration.B) at-the-money and has a long time until expiration.C) out-of-the-money and near expiration.D) deeply in the money.9 Which of the following statements concerning vega is most accurate? Vega is greatest when an option is:A) at the money.C) far out of the money.B) far in the money.D) closer to expiration.

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