
#1




RiskNeutral Valuation
Through exams and (very minimal) work exposure, I think I've come up with a working understanding of riskneutral vs. realworld valuation methods, but I don't really understand the purpose for RN. It seems that RN scenarios should generate a best estimate price if you take the average output, and that this is (at least theoretically) equal to the average RW output. The two should be equal on average, but the tail risk is better reflected in RW scenarios and basically nonsense for RN.
So, with that said, why use RN at all? If RW scenarios give you the same answer, and can be used for forecasting, producing loss percentiles, etc., why would you prefer using RN for any purpose? Is it just a model complexity thing, where you can get to the same answer in a less computationallyintensive approach? Or is there some theoretical reason that I'm missing?
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#2




We use RN when looking at blocks to buy, not RW. RW is used for modeling AG43 reserves, but RN is used in Europe for reserving under Solvency II. Additionally, RN is a proxy for the amount needed to fully hedge your risk. RW is wishful thinking in my book, hoping that the future will resemble the past, despite dramatically lower interest rates.

#3




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Carol Marler, "Just My Opinion" Pluto is no longer a planet and I am no longer an actuary. Please take my opinions as nonactuarial. My latest favorite quotes, updated Nov. 20, 2018. Spoiler: 
#4




Quote:
In my (granted elementary) understanding of this, the differences are: 1. Risk Neutral uses risk free rates, while Real World uses risk free rates plus some parameter to reflect the market price of the uncertainty of payoff. 2. Real World uses the "true" probabilities while Risk Neutral uses "risk neutral" probabilities. These probabilities work such that one can always be derived from the other. That being said, shouldn't the answers be the same? No matter whether you use real world or risk neutral interest rates, wouldn't you just adjust the probabilities accordingly so that the answer is the same? C4L
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#5




In the context of Actuarial Guideline 43 (AG43), RW scenarios are calibrated to past performance of various indices, such as the S&P 500. They are not calibrated to market prices.

#6




Quote:
2. RW has an added risk premium which represents various calibrations of what the company (usually provided by a third party) thinks represents realistic future economic scenarios. This is usually used in P&C. 
#7




Discounting expected values calculated using real world probabilities at risk adjusted rates gives the same value as risk neutral expected values discounted at risk free rates.
The former method underlies the CAPM which is used for primary assets and is referred to as equilibrium valuation. The latter is generally used for derivatives and is referred to as arbitrage free valuation. It is consistent with no arbitrage. The risk neutral approach facilitates valuation when the risk premia vary over time, and may depend upon the asset price.i 
#8




Does anyone agree with this analysis?
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Carol Marler, "Just My Opinion" Pluto is no longer a planet and I am no longer an actuary. Please take my opinions as nonactuarial. My latest favorite quotes, updated Nov. 20, 2018. Spoiler: 
#9





#10




Regulatory constraints would not allow you to value your liabilities using a heavily modified RW calibration
Also, even if you where allowed, why make your processes so onerous? Makes no sense to me. Also, you are going to also have to tinker with the swaption implied volatilities that have been calibrated specifically for the RW model in order to deduce a fit that combines with many other variables to give you a RN output. So once again, why do you want to make your life this hard? Makes no sense to me. 
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risk neutral, stochastic models 
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