# How to find value of arbitrage

If there is a stock with current price of 50 SR and there are only 2 possibilities where the stock can go up to 60 SR or 40 SR within 1 year time. Assume that the free risk interest rate is 10%.

Please answer the following questions and explain each step you take:

A)What is the expected call option price of this stock?

B)How arbitrage could happen if the price of call option is 6 SR. What is the value of arbitrage?

C)How arbitrage could happen if the price of call option is 7 SR. What is the value of arbitrage?

D)What is arbitrage and how could somebody (might) achieve that? Is it easy to do arbitrage in stock market? Why?

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B )I need help in B (How arbitrage could happen if the price of call option is 6 SR. What is the value of arbitrage?)

I need step by step with example so I can solve it

In d) Is it easy to do arbitrage in stock market? Why?

Can you help me to answer this i found some example but i am not shore it will be the answer

Thanks,

this my my trail

A)

A) current price= 50 SR

it will go to 60 SR or 40 SR

t=1

free risk interest = 10 %

we can find the stock return given a(rise or fall ) 20 %

from 50 to 60

((60 /50)-1)= .2 = 20 %

From 50 to 40

((40/50)-1)=-.2 =-20%

Know we need to found the probability of a raise necessary to achieve expected return of 10%

10%= probability of a raise*20% + (1- probability of a raise)*(-20%)

10%= 40% probability of a raise-20%

probability of a raise=30%/40%= 4/3

then the probability of a fall= ¼

call option = ((3/4)*(10 SR)+(1/4)*0)/1.1=6.83 SR

B)B) stock return=20%= 60 SR

current price= 50 SR

call option= 6 SR

value of arbitrage= 60 - 50 -6= 4 SR

#### Solution Preview

Dear Student,

Thank you for using BM.

Below are my answers.

Sincerely,

Anna Liza Gaspar

ANSWERS

QUESTION A

Assumption: Exercise price is 50 SR

u = 1+ [(60-50)/50] = 1.20

d = 1 - [(50-40)/50] = 0.80

S+ = Su = 50 (1.20) = 60

c+ = Max (0, S+ - X)

c+ = Max (0, 60 - 50) = 10

S- = Sd = 50 (0.80) = 40

c- = Max (0, S- - X)

c- = Max (0, 40 - 50) = 0

Then, calculate risk-neutral probability

(1 + r - d)/(u - d) = (1+.10-0.80)/(1.20-0.80) = 0.30/0.40 = 0.75

c = [(0.75x10)+(0.25x0)]/1.10=6.82 SR

QUESTION B

If the call option is selling for 6SR, the option is underpriced - a clear case of price not equaling value. Investors would exploit this opportunity by buying the option and selling short the ...