Hi, I am encountering some difficulty in understanding the issue of market consistent approaches, for instance market consistent calibration/valuation. I have quoted some parts of the notes below: Chapter 14 Page 8: "replicate the market prices of actual financial instruments as closely as possible, using an adjusted (risk neutral) probability measure." Chapter 17 Page 12: "If a market-consistent approach is used, either deterministically or stochastically, then the expected investment return can be set as the risk-free rate, irrespective of the actual underlying asset held." Chapter 17 Page 29: "The risk neutral" approach to such a valuation effectively involves the use of risk-free interest rates for the discount rates, ..." Chapter 20 Page 4: talks about market-consistent methodology which involves discounting projected cashflows at the risk-free rates I understand that the aim of market-consistent valuation is derive a value that is consistent with the current market values. For instance, a market-consistent valuation of a contract is one at which the market is willing to take up the liability for. However, I have difficulty understanding how is the risk-free rate related to this. From what i understand, for valuation, we usually consider the assets used to match the liability cashflows, and derive the market yield earned on these assets which will be used to discount the cashflows to find the reserves required. I would think that this would be market-consistent. I do not understand why risk-free rates are used instead. Could you please advice? Thanks a lot in advance.
The reasons why market consistent valuations use risk neutral probabilities and risk free rates is covered in CT8, eg we see that the risk free rate is used in the Black Scholes equation and risk neutral probabilities (often denoted as q to distinguish them from real world probabilities p) are used to calculate the probabilities of up and down steps in the binomial model. I don't want to repeat CT8 here (as it wouldn't score marks in ST2) but the basic idea is as follows. If I can find asset cashflows that exactly replicate the liability cashflows then they must surely have the same value. To exactly replicate, the assets would have to have no risk of going wrong, so we would use risk-free fixed interest government bonds to replicate our liability fixed cashflows. So it is the risk-free rate derived from bond yields that we use to calculate market values. The important thing to remember for the exam is that it doesn't matter which assets we actually hold in our portfolio. We could choose to mismatch, but we would still value our liabilities at risk-free rates. The course also considers some adjustments to this theory, eg liquidity premiums and risk premiums. Best wishes Mark
Q1 if we following market consistent approach and there interest rate bonds backing liability .How increase in yield will impact MC liability??
The yield on the assets we hold as no impact on a market-consistent valuation. However, if the risk-free rate increases then we would use this higher rate to discount our liabilities, so liabilities would go down. Higher yields also mean lower prices for bonds. Best wishes Mark
Thanks for this question and reply. I also found this confusing. If the best estimate liability is what a knowledgable party would take it on for, then wouldn't such a party invest in corresponding assets of higher return than risk free (albeit not with perfect matching or with counterparty risk) thus in the long run generate surplus from mainly investment returns exceeding risk free? Therefore it looks like the BEL is a rather cheap valuation & feels like a minimum acceptable price for selling the liabilities.
Yes, an insurer may well chose to invest in riskier assets. However, they will expect to gain a higher return to compensate them for this risk. They wouldn't receive this higher return if we'd already factored it into the price of the liabilities. Best wishes Mark
