chapter4金融工程

1oÙBinomial Model for Option
Pricing
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1.A stock price is currently$40.It is known that at the end of one month it will
be either$42or$38.The risk-free interest rate is8%per annum with continuous compounding.So the value of one-month European call option with a strike price of $39is.
2.A stock price is currently$50.It is known that at the end of six months it will
be either$45or$55.The risk-free interest rate is10%per annum with continuous compounding.So the value of a six-month European put option with a strike price of$50is.
3.A stock price is currently$100.Over each of the next two six-month periods it is
expected to go up by10%or down by10%.The risk-free interest rate is8%per annum with continuous compounding.The value of a one-year European call option with a strike price of$100is.
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1.The stock price is currently$80.The stock price annual up-move factor is1.15.The
risk-free rate is3.9%.The value of a two-year European call option with an exercise price of$62using a two-step binomial model is closest to()
A.$0.00
B.$18.00
C.$23.07
D.$24.92
2.The stock price is currently$80.The stock price will move up by15%each year.The
risk-free rate is3.9%.The value of a two-year European put option with an exercise price of$62using a two-step binomial model is closest to()
1
21oÙBINOMIAL MODEL FOR OPTION PRICING
A.$0.42
B.$16.89
C.$18.65
D.$21.05
3.JTE Corporation is a nondividend-paying stock that is currently priced at$49.An
analyst has determined that the annual standard deviation of returns on JTE stock is8%and that the annual risk-free interest rate on a continuously compounded basis is5.5%.Calculate the value of a6-month American call option on JTE stock with a strike price of$50using a two-period binomial model.()
A.$0.32
B.$0.65
C.$1.31
D.$2.97
4.Suppose a one-year European call option exists on SYZ stock.The current contin-
uously compounded risk-free rate is3%,and SYZ pays a continuous dividend yield of2%.Assume an annual standard deviation of3%.The risk-neutral probability of an up-move for the SYZ call option is()
A.0.67
B.0.97
C.1.00
D.1.03
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1.The Delta of a call option is negative,whereas the Delta of a put option is positive.
()
2.Riskless portfolios must earn the risk-free rate of interest.()
3.The value of an American option reflects the early exercise feature.()
4.The value of the comparable European put option can be calculated using put-call
parity.()
5.In a risk-neutral world the expected return on all assets is the risk-free rate.()
o!O K
1.A stock price is currently$50.Over each of the next two three-month periods it is
expected to go up by6%or down by5%.The risk-free interest rate is5%per annum with continuous compounding.What is the value of a six-month European call option with a strike price of$51?
3
2.For the situation considered in Problem1,what is the value of a six-month European
put option with a strike price of$51?Verify that the European call and European put prices satisfy put-call parity.If the put option were American,would it ever be optimal to exercise it early at any of the nodes on the tree?
3.A stock price is currently$40.It is known that at the end of three months it will be
either$45or$35.The risk-free rate of interest with quarterly compounding is8% per annum.Calculate the value of a three-month European put option on the stock with an exercise price of$40.Verify that no-arbitrage arguments and risk-neutral valuation arguments give the same answers.
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1.delta
2.risk-neutral world
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1.Explain the no-arbitrage and risk-neutral valuation approaches to valuing a European
option using a one-step binomial tree.。