Option pricing with random risk aversion

Based on a standard general equilibrium economy, we develop a framework for pricing European options where the risk aversion parameter is state dependent, and aggregate wealth and the underlying asset have a bivariate transformed-normal distribution. Our results show that the volatility and the skewness of the risk aversion parameter change the slope of the pricing kernel, and that, as the volatility of the risk aversion parameter increases, the (Black and Scholes) implied volatility shifts upwards but its shape remains the same, which implies that the volatility of the risk aversion parameter does not change the shape of the risk neutral distribution. Also, we demonstrate that the pricing kernel may become non-monotonic for high levels of volatility and low levels of skewness of the risk aversion parameter. An empirical example shows that the estimated volatility of the risk aversion parameter tends to be low in periods of high market volatility and vice-versa.

Forecasting The Pricing Kernel of IBNR Claims Development In Property-Casualty Insurance

Forecasting The Pricing Kernel of IBNR Claims Development In Property-Casualty Insurance

Forecasting The Pricing Kernel of IBNR Claims Development In Property-Casualty Insurance

Forecasting The Pricing Kernel of IBNR Claims Development In Property-Casualty Insurance

Pricing kernel factorization and recovery theorem

Recently, Ross proposed an idea, now known as the “Recovery Theorem,” that asserts that the real (physical) probability measure can be recovered from the market prices of derivatives. This work has generated a great deal of controversy in the finance literature. The purpose of this paper is to revisit the core idea of the recovery theorem and to examine its implications. In particular, issues concerning the so-called factorization of the pricing kernel will be examined from the viewpoint of the Flesaker–Hughston representation.