Calibration: calibration often refers to the process of adjusting the parameters of a financial model to match real-world market data. For example, when using an option pricing model like the Black-Scholes model, one may calibrate the model by adjusting parameters (such as volatility, interest rates, etc.) so that the model's predicted option prices closely match the actual market prices of options
For a stochastic model in which the economic assumptions vary, there are different approaches to the setting (‘calibration’) of these parameters. The most common are as follows:
- Risk Neutral calibration
- Real World Calibration
Risk Neutral Calibration
also known as ‘market-consistent’ calibration. The first step in a market-consistent calibration is to choose a number of financial instruments (usually derivatives) for which the price is known. A model is then built that can project the cashflows from these instruments in a range of scenarios. The parameters are then chosen in such a way that the average present value of the cashflows from the modelled simulations is sufficiently close to the known market price. The idea is that if the model can closely reproduce the observed prices of quoted assets, then the model should also provide market-consistent values for unquoted asset or liability cashflows.
Used for valuation purposes, particularly where there are options and guarantees. The focus of these calibrations is to replicate the market prices of actual financial instruments as closely as possible, using an adjusted (risk neutral) probability measure. In the risk-neutral world, the expected return on all assets is the risk-free rate.
Real World Calibration
With the real world calibration we determine the model parameters using our expectations of the future. These assumptions are then used to project the values of the assets and liabilities under each stochastic scenario. The focus of these calibrations is to use assumptions which reflect realistic ‘long-term’ expectations and which consequently also reflect observable ‘real world’ probabilities and outcomes.
Used for projecting into the future, for example for calculating the appropriate level of capital to hold to ensure solvency under extreme adverse future scenarios at a given confidence level.
Difference between both Calibrations
To see the difference between the two calibrations, consider two investments: bonds with a market price of 100 and equities with a market price of 100. If we used the risk neutral calibration, then the average present value of the cashflows from our model’s simulations would be 100 for each investment, ie the model has replicated the observed market prices. However, if instead we used the real world calibration, we would expect that on average the simulated cashflows from the equities would be higher than the bonds (as this is what usually happens in real life).