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.()

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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?