Is this financial market viable?

  • MHB
  • Thread starter WMDhamnekar
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In summary, the financial market in question has two risky stocks with initial values of $9.52 and $4.76 currency units. The simple interest is 5% during the period [0,1] and the stock values at time 1 can take three different values depending on the market states. The market viability is determined by the absence of arbitrage opportunities, which can be assessed by calculating the portfolio values for all possible states. The definition of "arbitrage opportunity" is a finance term and cannot be expected to be known by everyone.
  • #1
WMDhamnekar
MHB
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Consider a financial market with two risky stocks and such that values at t=0 $S^1_0= 9.52 $ currency units and $S^2_0=4.76$ currency units. The simple interest is 5% during the period [0,1].We also assume that during the period time 1, $S^1_1, S^2_1$ can take three different values depending on the market states $\omega_1, \omega_2,\omega_3$. $S^1_1(\omega_1)=20$ currency units, $S^1_1(\omega_2)=15$ currency units, $S^1_1(\omega_3)=7.5 $ currency units. $S^2_1(\omega_1)=6$ currency units, $S^2_1(\omega_2)=6$ currency units, $S^2_1(\omega_3)=4$ currency units. Is this market viable?
Answer. Viable financial merket means the market without arbitrage opportunities. Let $q_1$ and $q_2$ be the amounts invested in stock 1 and stock 2 respectively. Since the initial value of portfolio is zero, we should have $-9.52q_1$ and $-4.76q_2$ in the bank account.So our portfolio value at time 1 for all possible states are

$V_1(\omega_1)=10.004q_1+1.002q_2$$V_1(\omega_2)=5.004q_1+1.002q_2$

$V_1(\omega_3)=-2.496q_1-0.998q_2$


Now how to find out arbitrage opportunities?
 
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  • #2
What is the definition of "arbitrage opportunity"? That is a finance term, not mathematics so you cannot expect people here to know that.
 
  • #3
Dhamnekar Winod said:
Now how to find out arbitrage opportunities?
Contact Warren Buffett :)
 

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