The core reading in Chapter 15, section 3.3 states "It is worth noting that while many of the uses for such projection systems will involve market-consistent bases, for ALM purposes there will also need to be a real world basis to project asset returns (although the market-consistent basis will still be required for calculating the best estimate liability at future time points)." Could someone please explain this part? I am confused here because if you are using market-consistent basis then this means using risk-free returns and implied volatility for calibrations of ESG's and if you are using real-world then actual expectation of future will be used for returns and volatilities. How does this mean this ensure consistency between asset and liability projections if we are using different basis?
How about this for an example: Say that we are projecting our assets forward by one year using a real-world basis. Let's say we are doing 10,000 simulations that are calibrated to real-world returns (so the average investment return for each asset type across those 10,000 simulations should be our best estimate of what it is going to be over the next year). These simulations will each need to include a set of risk-free rates that will be applicable in one year's time. These will be used to calculate the liability values in one year's time. The simulated future risk-free yield curves will each need to be consistent with the 'real world' that we have projected in one year's time within that particular simulation.
Find some derivatives that are attached to that asset and that have observable market prices. Solve for the implied volatility within the appropriate closed form solution (eg Black-Scholes formula) that equates to those market prices. Hence giving the volatility that the market believes that asset has, and hence is priced into derivative trades.
