All materials on our website are shared by users. If you have any questions about copyright issues, please report us to resolve them. We are always happy to assist you.

Information Report

Category:
## Documents

Published:

Views: 114 | Pages: 9

Extension: PDF | Download: 13

Share

Related documents

Description

Hull: Options, Futures, and Other Derivatives, Ninth Edition
Chapter 13: Binomial Trees
Multiple Choice Test Bank: Questions with Answers
1. The current price of a non-dividend-paying stock is $30. Over the next six
months it is expected to rise to $36 or fall to $26. Assume the risk-free rate is
zero. An investor sells call options with a strike price of $32. Which of the
following hedges the position?
A. Buy 0.6 shares for each call option sold
B. Buy 0.4 shares for each call option sold
C. Sh

Tags

Transcript

Hull: Options, Futures, and Other Derivatives, Ninth EditionChapter 13: Binomial TreesMultiple Choice Test Ban: !uestions ith #ns ers
1.The current price of a non-dividend-paying stock is $30. Over the next six months it is expected to rise to $36 or fall to $6. !ssume the risk-free rate is ero. !n investor sells call options #ith a strike price of $3. hich of the follo#ing hedges the position%!.&uy 0.6 shares for each call option sold&.&uy 0.' shares for each call option sold(.)hort 0.6 shares for each call option sold*.)hort 0.6 shares for each call option sold !ns#er+ & The value of the option #ill ,e either $' or ero. f
∆
is the position in thestock #e reuire 36
∆
/'6
∆
so that
∆
0.'. it follo#s that 0.' shares should ,e purchased for each option sold..The current price of a non-dividend-paying stock is $30. Over the next six months it is expected to rise to $36 or fall to $6. !ssume the risk-free rate is ero. hat is the risk-neutral pro,a,ility of that the stock price #ill ,e $36% !.0.6&.0.(.0.'*.0.3 !ns#er+ ( The formula for the risk-neutral pro,a,ility of an up movement is
d ud e p
rT
−−=
n this case
u
=36/30
or
1.2
and
d
=26/30 =0.8667.
!lso
r
=0
and
T
=0.5.
The formula gives
p
=(1-0.8667/(1.2-0.8667) =0.4.
3.The current price of a non-dividend-paying stock is $30. Over the next six months it is expected to rise to $36 or fall to $6. !ssume the risk-free rate is ero. !n investor sells call options #ith a strike price of $3. hat is the value of each call option%!.$1.6&.$.0(.$.'*.$3.0 !ns#er+ !
The formula for the risk-neutral pro,a,ility of an up movement is
d ud e p
rT
−−=
n this case
u
=36/30
or
1.2
and
d
=26/30 =0.8667.
!lso
r
=0
and
T
=0.5.
The formula gives
p
=(1-0.8667/(1.2-0.8667) =0.4.
The payo2 from the call option is
$'
if there is an up movement and
$0
if there is a do#n movement. The value of the option is therefore
0.4×4 +0.6×0= $1.6
.
e do not do any discounting ,ecause the interest rate is ero.4'.The current price of a non-dividend-paying stock is $'0. Over the next year it is expected to rise to $' or fall to $35. !n investor ,uys put options #ith a strike price of $'1. hich of the follo#ing is necessary to hedge the position%!.&uy 0. shares for each option purchased&.)ell 0. shares for each option purchased(.&uy 0. shares for each option purchased*.)ell 0. shares for each option purchased !ns#er+ ( The payo2 from the put option is ero if there is an up movement and ' if there is a do#n movement. )uppose that the investor ,uys one put optionand ,uys
∆
shares. f there is
an
up movement the value of the portfolio is
∆
×
'
.
f there is a do#n movement it is #orth
∆
×
357'
.
These are eual #hen
37
∆
+
''
∆
or
∆
=
0.
.
The investor should therefore ,uy 0. shares foreach option purchased. .The current price of a non-dividend-paying stock is $'0. Over the next year it is expected to rise to $' or fall to $35. !n investor ,uys put options #ith a strike price of $'1. hat is the value of each option% The risk-free interest rate is 8 per annum #ith continuous compounding.!.$3.93&.$.93(.$1.93*.$0.93 !ns#er+ * The formula for the risk-neutral pro,a,ility of an up movement is
d ud e p
rT
−−=
n this case
r
=
0.0
,
T
=
1
,
u
':'01.0 and
d
35:'00.9 so that
p
0.56
and the value of the option is
0.56;070.';'4
e
-0.02×1
0.936.hich of the follo#ing descri,es ho# !merican options can ,e valued using a
,inomial tree%!.(heck #hether early exercise is optimal at all nodes #here the option is in-the-money &.(heck #hether early exercise is optimal at the <nal nodes(.(heck #hether early exercise is optimal at the penultimate nodes and the <nal nodes*.=one of the a,ove!ns#er+ ! >or an !merican option #e must check #hether exercising is ,etter than not exercising at each node #here the option is in the money. t is clearlynot #orth exercising #hen the option is out of the money45.n a ,inomial tree created to value an option on a stock? the expected return on stock is!.@ero&.The return reuired ,y the market(.The risk-free rate*.t is impossi,le to kno# #ithout more information !ns#er+ ( The expected return on the stock on the tree is the risk-free rate. This is an application of risk-neutral valuation..n a ,inomial tree created to value an option on a stock? #hat is the expected return on the option%!.@ero&.The return reuired ,y the market(.The risk-free rate*.t is impossi,le to kno# #ithout more information !ns#er+ ( The expected return on the option on the tree is the risk-free rate. This is an application of risk-neutral valuation. The expected return on all assets in a risk-neutral #orld is the risk-free rate.9.! stock is expected to return 108 #hen the risk-free rate is '8. hat is the correct discount rate to use for the expected payo2 on an option in the real #orld%!.'8&.108(.Aore than 108*.t could ,e more or less than 108 !ns#er+ *
The correct ans#er is *. There is no easy #ay of determining the correct discount rate for an optionBs expected payo2 in the real #orld. >or a call option the correct discount rate in the real #orld is often uite high and fora put option it is often uite lo# even negative4. The example in the text illustrates this. 10.hich of the follo#ing is true for a call option on a stock #orth $0!.!s a stockBs expected return increases the price of the option increases&.!s a stockBs expected return increases the price of the option decreases(.!s a stockBs expected return increases the price of the option might increase or decrease*.!s a stockBs expected return increases the price of the option on the stock stays the same!ns#er+ * The option price #hen expressed in terms of the underlying stock price is independent of the return on the stock. To put this another #ay? everything relevant a,out the expected return is incorporated in the stockprice.11.hich of the follo#ing are =OT true!.Cisk-neutral valuation and no-ar,itrage arguments give the same option prices&.Cisk-neutral valuation involves assuming that the expected return is the risk-free rate and then discounting expected payo2s at the risk-free rate(.! hedge set up to value an option does not need to ,e changed*.!ll of the a,ove!ns#er+ ( The hedge set up to value an option needs to ,e changed as time passes. ! and & are true.1.The current price of a non-dividend paying stock is $30. Dse a t#o-step tree tovalue a European call option on the stock #ith a strike price of $3 that expires in 6 months. Each step is 3 months? the risk free rate is 8 per annum#ith continuous compounding. hat is the option price #hen u 1.1 and d 0.9. !.$1.9&.$1.'9(.$1.69*.$1.9 !ns#er+ & The pro,a,ility of an up movement is

Recommended

Related Search

hadoop interview questions and answersibm c2090600 exam questions and answersdata science interview questions and answerseco 372 final questions and answersldr 531 final exam questions and answers300101 questions and answersquestions and answers pluginquestions and answersapache jmeter interview questions and answers1z0821 questions and answers

We Need Your Support

Thank you for visiting our website and your interest in our free products and services. We are nonprofit website to share and download documents. To the running of this website, we need your help to support us.

Thanks to everyone for your continued support.

No, Thanks