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Real-World Equity & Volatility Behavior: Implications for Economic Scenario Generation

In the risk-neutral world, all investments grow, on average, at the risk-free rate. However, in reality, risky positions earn a premium depending on their sensitivities to market factors. For instance, a call on an equity index is seen to earn a premium, while a put is seen to pay
a premium.

Thus, while risk-neutral dynamics are ideal for producing valuations and hedge ratios, risk must be assessed with reference to real-world dynamics. Real-world dynamics incorporate risk premia, and this has immediate consequences for the generation of economic scenarios by insurance companies.

This paper examines the differences between risk-neutral dynamics and real-world dynamics, and the important role of risk premia. We highlight why real-world dynamics are necessary for risk analysis and scenario generation, and also explore the roles of the equity premium and volatility premium in stochastic volatility models of equity markets.