I don’t understand what you mean. Specifically, I don’t understand what you are using ‘0’ for.
If the chance of paying is p, then the betting odds will reflect this with the assumption that the market is reasonably efficient.
For a simple fixed rate bet, for each dollar the company stakes, they win an additional p/(1−p) if they don’t payout over the time period (again assuming betting odds reflect the underlying probability).
Expected value (for the 1 dollar bet) is then:
(1−p)∗(p/(1−p))−p∗1=0
Of course, there is possibility for adverse selection/asymmetric information which could make the market somewhat less efficient.
I don’t understand what you mean. Specifically, I don’t understand what you are using ‘0’ for.
If the chance of paying is p, then the betting odds will reflect this with the assumption that the market is reasonably efficient. For a simple fixed rate bet, for each dollar the company stakes, they win an additional p/(1−p) if they don’t payout over the time period (again assuming betting odds reflect the underlying probability).
Expected value (for the 1 dollar bet) is then: (1−p)∗(p/(1−p))−p∗1=0
Of course, there is possibility for adverse selection/asymmetric information which could make the market somewhat less efficient.