Pricing Financial and Insurance Risks under Wang Transformation

In pricing financial risks, models are built on theoretical assumptions. Financial pricing models such as CAPM and Black-Scholes, usually depend on the assumption that future asset stock price follows the lognormal distribution and returns are normally distributed. Lack of the assumptions would have a serious inappropriate effect on pricing results. Thus, many researchers are trying to find a method of relaxing the underlying assumptions in these models. Further, there are many similarities between financial and insurance risks (e.g. options and stop-loss reinsurance contract). However, actuaries usually cannot use financial models for pricing insurance liabilities, because the loss amounts do not follow the distributions of the financial assets’ prices. Therefore, financial and insurance researchers are looking for a unified suitable frame for pricing all kinds of (financial) assets and (insurance) liabilities, with different types of probability distribution, whether traded or underwritten. In this research, we are going to introduce a new method to achieve this goal. In this approach, we transform the distribution of risk to a new distribution by Wang transformation with a risk parameter. The transformation applies on the distribution function as below; F* (x)=Φ[Φ-1(F(x)+α)] Where F is distribution functions of price and α is the risk parameter. Using this approach, it will be obtained a new technique for relaxing the distributional assumption in financial models. Wang's pricing framework recovers the results of CAPM and Black-Scholes model by necessary assumptions. Additionally, this approach presents a new method of empirical estimation and pricing financial derivatives consistent with real market conditions.