We study contagious defaults of banks by
applying a voting model.
The network of the banks are created by the relation, lending and borrowing among banks.
We introduce the response function from Merton model.
Using this response function we calculate the probability of default (PD) which
includes not only changes of asset values but also the effects of connected banks' defaults using
the mean field approximation.
If we approximate the normal distribution which Merton model uses by $\tanh$ function, we can obtain the kinetic Ising model which represents phase transition.
The asset volatility plays the role of temperature.
In the low temperature limit, the model becomes the threshold model.
We calculate PD which shows an effect of the situations around the bank as the additional PD using the self consistent equation.
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A Response function of Merton model and Kinetic Ising model
Masato Hisakado and Takuya Kaneko
posted on 13 December 2019
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