Market-consistency

[ActuarialKropotkin]

In the chapter on Setting Assumptions (1) the core reading states, "If a market-consistent approach is used, then the expected investment return can be set as the risk-free rate, irrespective of the actual assets held for both the deterministic and stochastic approaches (this is the 'risk neutral' calibration approach).

I do not understand the logic behind this. What I think I understand is that the real-world probability measure P can be transformed to a risk-neutral probability measure Q, which via the Girsanov and Radon-Nikodym theorems (that I do not quite grasp) allows us to calculate the Expected Value of cashflows under the Q-measure and to discount it at the risk-free rate. This is the rationale behind the Black-Scholes result.

Why does this extend to the pricing and valuation of cashflows contingent on death and/or survival? Are we also using an equivalent Q-measure here to convert from a real-world probability measure to a risk-neutral one? Am I missing something fundamental?

 

[Mark Willder]

In the chapter on Setting Assumptions (1) the core reading states, "If a market-consistent approach is used, then the expected investment return can be set as the risk-free rate, irrespective of the actual assets held for both the deterministic and stochastic approaches (this is the 'risk neutral' calibration approach).

I do not understand the logic behind this. What I think I understand is that the real-world probability measure P can be transformed to a risk-neutral probability measure Q, which via the Girsanov and Radon-Nikodym theorems (that I do not quite grasp) allows us to calculate the Expected Value of cashflows under the Q-measure and to discount it at the risk-free rate. This is the rationale behind the Black-Scholes result.

Why does this extend to the pricing and valuation of cashflows contingent on death and/or survival? Are we also using an equivalent Q-measure here to convert from a real-world probability measure to a risk-neutral one? Am I missing something fundamental?

Hi

Yes, we are using the same logic as in the Black-Scholes equation where we also use the risk-free rate. We also see the same approach in many other places in Subject CM2. For example, using binomial trees or the 5 step method also leads to using the risk-free rate, regardless of the actual underlying assets. Looking at cashflows contingent on mortality or survival doesn't really add any new concepts here. Considering the economic factors we still want to use risk-free rates in a market-consistent valuation.

Considering the non-hedgeable risks (eg mortality/longevity) is dealt with separately, eg through the cost of capital approach for the risk margin.

Best wishes

Mark