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Hull: Options, Futures, and Other Derivatives, Ninth Edition
Chapter 19: The Greek Letters
Multiple Choice Test Bank: Questions with Answers
1. A call option on a stock has a delta of 0.3. A trader has sold 1,000 options.
What position should the trader take to hedge the position?
A. Sell 300 shares
B. Buy 300 shares
C. Sell 700 shares
D. Buy 700 shares
Answer: B
When the stock price increases by a small amount, the option price increases
by 30% of this amount. The trader therefore has a hedged

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Hull: Options, Futures, and Other Derivatives, Ninth EditionChapter 19: The Greek Letters Multiple Choie Test !ank: uestions #ith $ns#ers
1.A call option on a stock has a delta of 0.3. A trader has sold 1,000 options. What position should the trader take to hedge the position?A.Sell 300 sharesB.Buy 300 sharesC.Sell 700 shares.Buy 700 shares Ans!er BWhen the stock price increases #y a s$all a$ount, the option price increases #y 30% of this a$ount. &he trader therefore has a hedged position if he or she #uys 300 shares. 'or s$all changes the gain or loss on the stock position is e(ual and opposite to the loss or gain on the option position. ).What does theta $easure?A.&he rate of change of delta !ith the asset priceB.&he rate of change of the portfolio *alue !ith the passage of ti$eC.&he sensiti*ity of a portfolio *alue to interest rate changes.+one of the a#o*eAns!er B &heta $easures the rate of change in the *alue of a portfolio !ith the passage of ti$e.3.What does ga$$a $easure?A.&he rate of change of delta !ith the asset priceB.&he rate of change of the portfolio *alue !ith the passage of ti$eC.&he sensiti*ity of a portfolio *alue to interest rate changes.+one of the a#o*eAns!er A a$$a $easure the rate of change of delta !ith the asset price.-.What does *ega $easure?A.&he rate of change of delta !ith the asset priceB.&he rate of change of the portfolio *alue !ith the passage of ti$eC.&he sensiti*ity of a portfolio *alue to interest rate changes.+one of the a#o*eAns!er
ega $easures the rate of change of the *alue of the portfolio *alue !ith *olatility./.What does rho $easure?A.&he rate of change of delta !ith the asset priceB.&he rate of change of the portfolio *alue !ith the passage of ti$eC.&he sensiti*ity of a portfolio *alue to interest rate changes.+one of the a#o*eAns!er Cho $easures the rate of change of the *alue of the portfolio !ith interest rates. 2sually a parallel shift in interest rates is considered.4.Which of the follo!ing is true?A.&he delta of a 5uropean put e(uals $inus the delta of a 5uropean callB.&he delta of a 5uropean put e(uals the delta of a 5uropean callC.&he ga$$a of a 5uropean put e(uals $inus the ga$$a of a 5uropean call.&he ga$$a of a 5uropean put e(uals the ga$$a of a 5uropean call Ans!er &he delta of a put on a non6di*idend6paying stock e(uals the delta of the call$inus one. &he ga$$a of a put e(uals the ga$$a of call e*en !hen there are di*idends.7.A portfolio of deri*ati*es on a stock has a delta of )-00 and a ga$$a of 10.An option on the stock !ith a delta of 0./ and a ga$$a of 0.0- can #etraded. What position in the option is necessary to $ake the portfolio ga$$aneutral?A.8ong position in )/0 optionsB.Short position in )/0 optionsC.8ong position in )0 options.Short position in )0 options Ans!er A &he options $ust ha*e a ga$$a of 910 to neutrali:e the ga$$a of the portfolio. 5ach option has a ga$$a of 0.0-. ;ence a long position of 10<0.0- = )/0 options is re(uired.>.A trader uses a stop6loss strategy to hedge a short position in a three6$onth call option !ith a strike price of 0.7000 on an echange rate. &he current echange rate is 0.4@/0 and *alue of the option is 0.1. &he trader co*ers the option !hen the echange rate reaches 0.700/ and unco*ers i.e., assu$es anaked position if the echange rate falls to 0.4@@/. Which of the follo!ing is
+& true?A.&he echange rate trading $ight cost nothing so that the trader gains 0.1 for each option soldB.&he echange rate trading $ight cost considera#ly $ore than 0.1 for each option sold so that the trader loses $oneyC.&he present *alue of the gain or loss fro$ the echange rate trading should #e a#out 0.1 on a*erage for each option sold.&he hedge !orks reasona#ly !ell Ans!er A good hedging syste$ !ill ensure that the cost of selling an option is closeto its theoretical *alue. &he stop6loss hedging procedure does not ha*e thisproperty. t can lead to the option costing nothing or costing considera#ly$ore than its theoretical *alue. n a*erage the cost of the option is its Black6Scholes *alue, #ut there is a !ide *ariation. is the correct ans!er. @.aintaining a delta6neutral portfolio is an ea$ple of !hich of the follo!ing A.Stop6loss strategyB.yna$ic hedgingC.;edge and forget strategy.Static hedgingAns!er B elta6neutral hedging is an ea$ple of dyna$ic hedging. &he hedge has to #e adDusted periodically. n theory, to $aintain a delta6neutral hedge, the hedge $ust #e adDusted continuously.10.Which of the follo!ing could +& #e a delta6neutral portfolio?A.A long position in call options plus a short position in the underlyingstockB.A short position in call options plus a short position in the underlyingstockC.A long position in put options and a long position in the underlying stock.A long position in a put option and a long position in a call optionAns!er BCalls ha*e a positi*e delta. Euts ha*e a negati*e delta. A long stock position has a positi*e delta. A short stock position has a negati*e delta. B cannot #e delta neutral i.e., ha*e a delta of :ero #ecause #oth parts of the portfolio ha*e a negati*e delta.11.Which of the follo!ing is +& true a#out ga$$a?A.A highly positi*e or highly negati*e *alue of ga$$a indicates that aportfolio needs fre(uent re#alancing to stay delta neutral
B.&he $agnitude of ga$$a is a $easure of the cur*ature of the portfolio*alue as a function of the underlying asset priceC.A #ig positi*e *alue for ga$$a indicates that a #ig $o*e$ent in theasset price in either direction !ill lead to a loss.A long position in either a call or a put has a positi*e ga$$a Ans!er CC is not true. &he change in the *alue is a gain of 0./
Γ∆
S
)
. &here is a gain fro$ a #ig $o*e$ent !hen ga$$a is positi*e and a loss fro$ a #ig $o*e$ent !hen ga$$a is negati*e. 1).a$$a tends to #e high for !hich of the follo!ingA.At6the $oney optionsB.ut6of6the $oney optionsC.n6the6$oney options.ptions !ith a long ti$e to $aturity Ans!er Aa$$a tends to #e high for at6the6$oney options. See 'igure 1@.@.13.Which of the follo!ing is true for a call option on a non6di*idend6paying stock !hen the stockFs price e(uals the strike price?A.t has a delta of 0./B.t has a delta less than 0./C.t has a delta greater than 0./ .elta can #e greater than or less than 0./Ans!er C &he delta is
N
d
1
!here
T T r K S
d
σσ++=
)2/()/ln(
201
'ro$ this it can #e seen that, !hen
S
0
=
K
,
d
1
is
σσ+
T r
)2/(
2
&his is al!ays positi*e. ;ence delta is al!ays greater than 0./.

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