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  #11  
Old 04-06-2017, 11:11 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.
This was my understanding as well. If this is the case, though, what's the advantage to using risk-neutral valuation? If real-world gives you the same answer, and you can use actual cash flows (so each scenario produces realistic projection results), why ever use RN (which uses risk-adjusted / unrealistic cash flows)? It seems like RW gets you to the same place, and is more versatile.

Obviously, certain regulations will mandate one method or the other, but I just mean from a theoretical point of view.
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Old 04-06-2017, 11:31 PM
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So once again, why do you want to make your life this hard? Makes no sense to me.
I'm not advocating the use of a heavily modified RW calibration. I was just trying to understand one of the earlier posts which referred to RW as "wishful thinking", so I wanted some clarification since I would expect a RN method to yield the same answer.
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  #13  
Old 04-06-2017, 11:41 PM
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why ever use RN (which uses risk-adjusted / unrealistic cash flows)?
Might RN scenarios be advantageous when you're dealing with an asset or liability that is not traded on the market - i.e. Insurance Cashflows?

i.e. How do you know what the "risk premium" is over the risk free rate on a set of Insurance Cashflows? In this case, it makes sense to me that a RN methodology may be used.
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Old 04-06-2017, 11:50 PM
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This was my understanding as well. If this is the case, though, what's the advantage to using risk-neutral valuation? If real-world gives you the same answer, and you can use actual cash flows (so each scenario produces realistic projection results), why ever use RN (which uses risk-adjusted / unrealistic cash flows)? It seems like RW gets you to the same place, and is more versatile.

Obviously, certain regulations will mandate one method or the other, but I just mean from a theoretical point of view.
I mentioned this in my post. When Black and Scholes first tried to value options they tried it in a CAPM framework, but realized that for options, the beta varies with the stock price making it a random variable. The discounting problem is solved by moving to the risk neutral framework.

A problem with discounting at a risk adjusted rate is specifying the correct risk adjusted rate. CAPM is nice in theory but even some academics don't believe it has anything to do with reality.

There is a third approach to risk adjustment which is to adjust the cash flows to certainty equivalents and discounting at the risk free rate. This is used mainly theoretical work as it requires specifying a utility function that reflects the risk of the entire market.
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Old 04-07-2017, 04:44 PM
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I mentioned this in my post. When Black and Scholes first tried to value options they tried it in a CAPM framework, but realized that for options, the beta varies with the stock price making it a random variable. The discounting problem is solved by moving to the risk neutral framework.

A problem with discounting at a risk adjusted rate is specifying the correct risk adjusted rate. CAPM is nice in theory but even some academics don't believe it has anything to do with reality.
this is it, pretty much, don't worry so much about the other mumbo jumbo you've seen in other posts.

john hull does a good job of explaining this stuff in options, futures, and other derivatives

also read this: https://papers.ssrn.com/sol3/papers....act_id=1395390

towards the end:

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The nice aspect of this pricing approach is that we no longer need to estimate the parameter μ ["real world" brownian motion drift term, or return with risk premium]. This is the whole merit of risk-neutral pricing. The quality of our arbitrage-free pricing now depends on our ability to estimate σ [volatility].
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Old 04-07-2017, 09:49 PM
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Thanks, everyone, for your responses. That makes a lot of sense, actually. I guess I was getting too caught up in the theory and completely forgot that the risk premium is not a given. If you knew the correct risk-adjusted discount rate, the two methodologies would give you equivalent expected PV's, but that's a pretty big if.
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Old 04-08-2017, 07:12 AM
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Don't mean to reintroduce confusion here, but while RN scenarios have a straightforward interest rate (I.e. Just the risk free rate), how do we determine what the risk neutral probabilities are to use within RN scenarios?
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  #18  
Old 04-08-2017, 12:47 PM
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Originally Posted by Academic Actuary View Post
I mentioned this in my post. When Black and Scholes first tried to value options they tried it in a CAPM framework, but realized that for options, the beta varies with the stock price making it a random variable. The discounting problem is solved by moving to the risk neutral framework.

A problem with discounting at a risk adjusted rate is specifying the correct risk adjusted rate. CAPM is nice in theory but even some academics don't believe it has anything to do with reality.

There is a third approach to risk adjustment which is to adjust the cash flows to certainty equivalents and discounting at the risk free rate. This is used mainly theoretical work as it requires specifying a utility function that reflects the risk of the entire market.
Thanks for insights. I have finally figured out the misunderstanding I had about RN valuations. Somebody once told me (and I guess I believed it) that for RN the modeler assumed that investments would pay interest at the risk-free rate. I never could figure out how that would work, but now I see that it never was supposed to do so.
I feel so embarrassed.
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Old 04-08-2017, 12:55 PM
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this is it, pretty much, don't worry so much about the other mumbo jumbo you've seen in other posts.

john hull does a good job of explaining this stuff in options, futures, and other derivatives

also read this: https://papers.ssrn.com/sol3/papers....act_id=1395390

towards the end:
Hull is being overly simplistic here as RN pricing also depends on what interest rate model you end up using.

Estimating the volatilities in the two (or more) factor case is problematic, which is why a lot of models have problems when trying to replicate existing market instruments.
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Old 04-11-2017, 04:46 AM
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hull is a good starting point
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