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# 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%.

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.

Sincerely,
Anna Liza Gaspar

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 ...

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