# One period model Fincial Market - Arbitrage

• Apr 11th 2012, 07:08 AM
LHeiner
One period model Fincial Market - Arbitrage
Hi

Can you help me with the following, i think it is pretty easy but I don't get it:

Consider a discrete one period model of the financial market. We have a risk-free bond and a stock. The bond hast at time 0 a value of 1 and at time 1 $\displaystyle$1+r$$, , \displaystyle r>-1, the stock has at time 0 a value of 3 and with positive probability one of the three values (3 possible states) \displaystyle \omega_1=1, \omega_2=2, \omega_3=3$$. so we have the following equation system:
$\displaystyle \begin{pmatrix}1 & 1 &1 \\ 1& 2 &3\end{pmatrix}\bold{x}=\begin{pmatrix}\frac{1}{1+ r}\\3\end{pmatrix}$

The question is to determine all interest rates $\displaystyle$r$$for which there is no arbitrage and to give an arbitrage opportunity for one of the other \displaystyle r$$.

In a one-period model, I normally look at the equation sytem and determine if we have a unique solution, but how can this be done in this example?

Thank you