EBK CORPORATE FINANCE
EBK CORPORATE FINANCE
11th Edition
ISBN: 8220102798878
Author: Ross
Publisher: YUZU
Question
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Chapter 23, Problem 8QP
Summary Introduction

To determine: The price of put option.

Binomial Model:

Binomial model is the option of the modal in which price of the modal move according to the market situation. If the price of the option rises, it means that economic scenario is good and vice versa.

Expert Solution & Answer
Check Mark

Explanation of Solution

Given,

Current stock price is $82.

Standard deviation on stock return is 70%.

Strike price of the option is $90.

Risk free rate is 5%.

The price of the put option will be three by using one-month steps.

Calculate the price of the put value stock,

Putvalue=[PRise(C0)+PFall(C0)]1+Riskfreerate

Where,

  • PRise is the rise in the price.
  • C0 is the put value of the option.
  • PFall is the fall in price.

Substitute, 0.46 for the PRise (working note), $0 for the put value option, 0.54 for the PFall , (working note), and 0.42% for the risk free rate,

Putvalue(1)=[0.46($0)+0.54($7.01)](1+0.0042)=$3.78541.0042=$3.77

Substitute, 0.46 for the PRise , $7.01 for the put value option C1 , 0.54 for the PFall , and 0.42% for the risk free rate and 55.401 for the put value of the C2 ,

Putvalue(2)=[0.46($7.01)+0.54($55.401)](1+0.0042)=$33.591.0042=$33.0025

Substitute 0.46 for the PRise , $266.54 for the put value 1 and $2333.88 for the put value 2 and 0.42% for the risk free rate.

Putvalue(3)=[0.46($266.54)+0.54($2,333.88)](1+0.0042)=$122.61+$1260.31.0042=$1,382.911.0042=$1,377.126

Working Notes:

To calculate the value of the stock by binomial modal, first find the value of the U and D,

Calculate the value of the U,

U=eσn

Where,

  • Percentage of the price rice up is U.
  • Exponential factor is e (2.718)
  • Standard deviation is σ .
  • Number of the month is n

U=2.7180.7012=2.7180.202073=1.2239

Calculate the value of the D,

D=1U

Where,

  • D is the percentage of decrease in price of the house.
  • U is the percentage of increase in price of the house.

D=11.2239=0.8170

Calculate the monthly risk free rate,

Monthlyriskfreerate=Annualriskfreerate12=5%12=0.42%

Calculate the probability of price increase,

Riskfreerate=(PRise)(ReturnFall)+(PFall)(ReturnFall)0.42%=(PRise)(22.39)%+(1PRise)(18.3%)PRise=46%

Calculate the probability of price decrease,

PFall=(1PRise)=10.46=0.54

Calculate the stock price after one month in case, increase or decrease,

Stockprice=Currentprice×Increaseinstockprice=$83×1.2239=$101.58

Calculate the stock price when price decrease,

Stockprice=Currentprice×Decreaseinstockprice=$83×0.8170=$67.81

There will be four value of the stock in the two months, two values from the stock up and two values from the stock down,

Calculate the stock price after two month in case of stock up,

Stockprice=Currentprice×Increaseinstockprice×Increaseinstockprice=$83×1.2239×1.2239=$124.32

Increase in the stock price is the 1.2239 for one month. Here, stock price is being to calculate two months that is why it will be multiplied two times

Calculate the put option value in this case,

C1=max(SX,0)

Where,

  • Call value at the beginning is C0 .
  • Strike price is X.
  • House price at n period is S.

C1=Max($90$124.32)=$34.32

Calculate the value of the stock when price decrease,

Stockprice=Currentprice×Decreaseinstockprice×Increaseinstockprice=$83×0.8170×1.2239=$82.99

Calculate the put option value in this case,

C0=max(SX,0)

C2=Max($90$82.99)=$7.01

Calculate again the stock price after one month in case, increase or decrease

Stockprice=Currentprice×Increaseinstockprice×Decreaseinstockprice=$83×1.2239×0.8170=$82.99

Calculate the put option value in this case,

C0=max(SX,0)

C2=Max($90$82.99)=$7.01

Calculate the value of the stock when price decrease,

Stockprice=Currentprice×Decreaseinstockprice×Decreaseinstockprice=$83×0.8170×0.8170=$55.401

Decrease in the stock price is the 0.8170 for one month. Here, stock price is being to calculate two months that is why it will be multiplied two times

Calculate the put option value in this case,

C0=max(SX,0)

C2=Max($90$55.401)=$34.6

Conclusion

Hence, price of the put option is $9,738.80.

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