QuoteOriginally posted by: joeykRe the topic of this FAQ, I have heard:"Risk Neutral pricing underprice options because risk free rate is definitely lower than expected returns.""The BS formula and the dynamic hedging ensures that at every moment your portfolio has no risk"Anyone reading my pontifications on this subject in this thread and others would know that my position has been that1. Risk-neutral valuation works because the market will have already priced in any risk premium.2. Any future expected risk premium will affect an option value only through higher moments (e.g. volatility).It's now time for me to revise my position. I am now of the opinion that the market does is not anything like efficient enough to price in the risk premium and therefore that risk-neutral valuation will not enable the profits that can come from having a better model of expected value. However, if you are a market maker and are tightly limited in your bid/ask spread then you had better continue to use risk-neutral pricing or you will get creamed. Those of us who are not market-makers have the luxury of choosing whether we want to buy or sell or neither and can therefore make use of better models. If we want to make a quote it will be max[risk-neutral,ourvalue] to sell and min[risk-neutral,ourvalue] to buy. But then, of course, we will be lucky to find a counter-party, so we may have to settle for the best price we can get thereby exposing ourselves to an inability to close our position at an appropriate price later. As regards joeyk's quote, I would say this is likely correct, under most circumstances, for any market where the underlyings have a positive risk premium (e.g. stocks). If the current market underprices the underlying, then risk-neutrality will underprice the call and, by put-call parity it will also underprice the put. If the current market overprices the underlying then risk-neutrality will underprice the put and, by put-call parity, it will also underprice the call. However, there is exposure in this due to market friction (e.g. bid/ask spread) because this can cause a violation of put-call parity between buying and selling. So any expectation to profit from this (other than by sheer luck) will depend on a sufficiently small bid/ask spread relative to the pricing error from risk-neutrality both when entering a position and when exiting (unless holding until expiration). Edit: I should have added that underpricing of options using risk-neutrality depends on the same volatility being used. In practice, of course, risk-neutral pricing can restore value by increasing implied volatility. So joeyk's quote would better be expressed as "risk-neutral pricing requires an over-estimate of volatility in order to avoid under-pricing when a risk premium is present".
Last edited by Fermion
on October 22nd, 2009, 10:00 pm, edited 1 time in total.