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Risk Neutral valuation

Josu

Joined
4/28/10
Messages
10
Points
11
Hi everybody...

Have some question I've been wondering to know for some days regarding the basic risk neutral valuation method, under which a price of a derivative is obtained via the well known discounted value of the Risk neutral expected payoff at mat.

I've understood where do this result comes from, in the basic B-S case with deterministic money market account numeraire, via the replicating self-financing portfolio consisting on the underlying asset and the cash (in the result proof, assets lognormal distribution was used to characterize the discounted value of the portfolio was a martingale, which leads the result ) . The question is, do u need the asset to be lognormally distributed in order to apply E[ payoff] to price the derivative? Because it seems like the formula is sometimes used as a "maxim" in a risk neutral world, rather than some proven result ( like I described above ).

The rule Price= D(t,T) * E[payoff] is always assumed as the method to value, but I don't know if there should be also the lognormal assumption, or , like I said, this is just a "maxim" in the pricing theory.

Thanks!!!!

---------- Post added at 07:53 PM ---------- Previous post was at 06:37 PM ----------

Oh sorry! just realized all I need to understand this is Harrison & Kreps result regarding martingales ( "Martingales and Arbitrage in Multiperiod Securities Market" .
I've been looking for it and cannot find it... does anybody know any book where this result is explained?
 
Do you want the paper written by Harrison ?

"Martingales and Arbitrage in Multiperiod Securities Market" ?
 
Why don't you share it in the 'downloads' section, so the rest of the quantnet-world can see what Harrison & Kreps actually proved?

I don't know the answer to Josu's question, but I do know that historically, 'taking the risk-neutral expectation' was used as a rule rather than being derived from something. Bachelier's "L'esperance mathematique du speculateur est nul" led him to price options as we now know it, taking expectation with respect to some artificial measure. He used (plain) brownian motion as a model of stock price. On the other hand, I think he was lucky, because he used "true" (forward) prices instead of spot prices (similar as Black did), as he didn't mention "risk free interest rate" in his derivation, rather he used an equilibrium approach.

If anyone has his thesis in pdf, please share it! Thanks.
 
Mr Doe said:
Why don't you share it in the 'downloads' section, so the rest of the quantnet-world can see what Harrison & Kreps actually proved?

I don't know the answer to Josu's question, but I do know that historically, 'taking the risk-neutral expectation' was used as a rule rather than being derived from something. Bachelier's "L'esperance mathematique du speculateur est nul" led him to price options as we now know it, taking expectation with respect to some artificial measure. He used (plain) brownian motion as a model of stock price. On the other hand, I think he was lucky, because he used "true" (forward) prices instead of spot prices (similar as Black did), as he didn't mention "risk free interest rate" in his derivation, rather he used an equilibrium approach.

If anyone has his thesis in pdf, please share it! Thanks.
Click to expand...

I think there might be sharing restrictions on journal articles that require subscriptions. I have bachelier's thesis...in french. lol It was translated in English and published in some books I think.

http://archive.numdam.org/article/ASENS_1900_3_17__21_0.pdf
 
You don't need to. But Geometric Brownian Motion is the most popular model to reflect stock price movement nowadays.
 
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