QuoteOriginally posted by: snooper77To me, the term "risk-neutral" is somewhat misleading. I rather see it as "growth-neutral", and here's my explanation:The underlying asset is expected to grow at its growth rate mu. However, today it has the price it has today, i.e., if we were to price the underlying asset based on real expectations (i.e., growing at mu), it is mispriced itself. Therefore, we also have to price derivatives by not considering their final payoff, but by the payoff as if it were today, i.e., without any growth priced in. As a seconds step, we have to discount this expectation to today using the risk-free rate because the payoff will not happen until expiration.I think that is an accurate description except that, instead of "i.e., without any growth priced in", I would write "because the present value of the expected risk compensation is already priced into the underlying (and its future contract)"QuoteTherefore, in my opinion, risk-neutral valuation should not be explained by "replace the growth rate by the risk-free rate", but rather "dump the growth rate altogether and discount the expected payoff using the risk-free rate". In fact, this is the same thing, but the latter just makes more sense to me intuitively.Any comments on this way of seeing it?I don't agree with this. Instead of "dump the growth rate altogether" I would rather say, "replace the expected value by the risk-free expected value" or "dump the present value of the expected risk compensation altogether". The real growth rate (and future risk compensation) may well still affect the shape of the risk-neutral distribution (i.e. variance and higher moments).
Last edited by Fermion
on October 22nd, 2008, 10:00 pm, edited 1 time in total.