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How to Find Value of Arbitrage

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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.

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.

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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 underlying. This would generate cash up front. The number of ...

Solution Summary

The solution discusses how to find value of arbitrage.

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Arbitrage Opportunity

Suppose that the premium on a European put option, p = $3. The time to maturity, T = 1 year. The strike price is $20. The stock price of the underlying common stock is $12 today. The risk-free interest rate is 8% per annum. The stock does not pay dividends.

Observe that there is an arbitrage opportunity.

Clearly state what the trader would do to make a profit.

Make sure that you demonstrate the relation that must be satisfied to eliminate the arbitrage opportunity

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