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frenchX
Topic Author
Posts: 5911
Joined: March 29th, 2010, 6:54 pm

### Derivative pricing with cumulative prospect model

We all know the standart derivative pricing method by replicating a portfolio as a perfect hedge in a complete market. In incomplete markets, one of the method is to use utility theory to price a derivative. It is well know that utility theory as a lot of flaws so why not trying to apply the idea of behavioural finance into derivative pricing.CPT characteristics are the following ones:1) A reference point (or neutral outcome/benchmark/breakeven point/status quo) in wealththat defines gains and losses2) A value function (which replaces the notion of utility function), concave for gainsand convex for losses (such a function is called S-shaped) and steeper for losses thanfor gains3) A probability weighting function that is a nonlinear transformation of probabilitymeasure, which inflates a small probability and deflates a large probabilityIt seems that it change drastically the portfolio selection choice (it can be ill posed in some case) but what about derivative pricing in this case ?

Paul
Posts: 10794
Joined: July 20th, 2001, 3:28 pm

### Derivative pricing with cumulative prospect model

These things are fine for one derivative, but you hit major problems as soon as you want to value portfolios (as you should).P

frenchX
Topic Author
Posts: 5911
Joined: March 29th, 2010, 6:54 pm

### Derivative pricing with cumulative prospect model

I agree that there may be some aggregation problem. This paper says :"Cumulative Prospect Theory (CPT) has been used as a possible explanation of aggregate pricing anomalies like the equity premium puzzle. This paper shows that, unlike in expected-utility models, a complete market is not sufficient to guarantee that the market portfolio is efficient, and that the standard representative-agent analysis is valid. The separation or mutual fund theorems hold only under very restrictive conditions for CPT investors. Without them, aggregation breaks down, and assets are not necessarily priced as if there were one investor who behaved according to CPT. Under more limited conditions, the market portfolio can be efficient in a complete market with equally probable states. But in this case, individual CPT investors behave in the aggregate like a standard expected utility investor. Similarly, when faced with elliptically distributed assets, the CAPM holds for any combination of CPT investors and expected utility maximizers."(ref here http://cfr.ivo-welch.info/2014/ingersoll-cpt-2014.pdf)But in fact the fact that the "representative agent" does not hold is maybe a good point (I hate the idea that you could model the collective behaviour of an ensemble of irrational guys by a single rational fictive character). Portfolio aggregation are also more difficult due to the nonlinear nature of the stuff but I remember that you have nothing against nonlinearity For me there is just a funny stuff, is that the authors still consider the maximization of the expectation as if the investor "rationnally" maximize their "irrational utility". Very funny In my opinion, people (not professional investor) TRY TO MAXIMIZE (and not fully maximize) their FUTURE EXPECTATION CONDITIONAL TO THEIR PRESENT BELIEF (which is not the same that the mathematical expectation with all the available information). But CPT is a good start.
Last edited by frenchX on September 4th, 2013, 10:00 pm, edited 1 time in total.

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