Treasury Finance and Development Banking: A Guide to Credit, Debt, and Risk, + Website

APPENDIX F

Replication Leading to Risk-Neutral Probabilities

With the idea of stressing the difference between the valuation of financial and nonfinancial instruments as introduced in Section 7.2.1, let us consider a simple example not linked to the financial world. Let us consider an insurance company that pays out $1,000 in case of loss of luggage; statistically it has been found that 10% of the time someone loses a suitcase. A price for this product would then be $100 since it is the probability of the luggage being in the state lost times the payout when this is the case. If the insurance company were to charge $101 to every customer, in the long run they would make a profit: every 10 customers they would collect $1,010, pay out $1,000 to the unfortunate one, and gain $10 profit. The problem is that this is true for a very large number of insurance contracts sold, which realistically will be sold only over time. What if the number of insurance contracts sold is not large enough? What if over two years 2,000 insurance contracts are sold at regular interval and, as expected, 20 suitcases are lost, but all are lost in the first three months? This would create a serious liquidity problem. This approach is based on assigning probabilities based on the distribution of the real-world measure; this approach is chosen by insurance companies (which try to protect themselves by being very conservative, that is, pessimistic, about the possible scenarios) but not in finance.

Simplifying ...