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Old 04-04-2017, 10:41 PM
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Default Risk-Neutral Valuation

Through exams and (very minimal) work exposure, I think I've come up with a working understanding of risk-neutral vs. real-world 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 computationally-intensive approach? Or is there some theoretical reason that I'm missing?
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Old 04-05-2017, 05:42 PM
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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.
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Old 04-05-2017, 07:36 PM
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Old 04-06-2017, 12:17 AM
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Originally Posted by Numbers Nerd View Post
RW is wishful thinking in my book, hoping that the future will resemble the past, despite dramatically lower interest rates.
Shouldn't the same answer be achieved whether you use risk neutral or real world scenarios?

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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Old 04-06-2017, 04:48 PM
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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.
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Old 04-06-2017, 06:06 PM
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Quote:
Originally Posted by Celtics4Life View Post
Shouldn't the same answer be achieved whether you use risk neutral or real world scenarios?

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
1. When modelling asset returns with RN there is no risk premium. So basically if you start with $1, run 10,000 stochastic sims over the next year in regards to your asset returns, take the average of all the sims, and then discount back at the RFR, you should end up with the initial $1 plus/minus a small standard error.

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.
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Old 04-06-2017, 06:29 PM
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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
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Old 04-06-2017, 07:08 PM
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Quote:
Originally Posted by Celtics4Life View Post
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
Does anyone agree with this analysis?
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Old 04-06-2017, 07:10 PM
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Does anyone agree with this analysis?
I do. Read my previous post.
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Old 04-06-2017, 07:17 PM
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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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