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?
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?
