ボラティリティ・スマイル

最近オプション取引を学びながら以上の単語を見ました。
The Black-Scholes formula for option pricing is based on the assumption of geometric Brownian motion of stock returns. Stock returns are considered to be normally distributed about a mean, and volatility is assumed constant over the lifetime of the option. However, one can use market prices and the Black-Scholes formula to compute the implied volatility indicated by the market price. While computing this directly via algebra is not possible (Black-Scholes is C = SN(d1)-e^(-r(T-t))KN(d2)), it can be computed by iterative processes like the Newton-Raphson method (drawing tangent lines to actual curve and improving guesses at implied volatility). Computing the implied volatilities and plotting against the ratio of strike to spot yields a graph known as the volatility smile.
This is useful, as it suggests that a constant volatility model may not yield accurate prices, assuming an efficient market (no arbitrage opportunities). As the graph slopes upward as strike/spot decreases (put option is out of the money), and higher volatility leads to higher prices, the market price of out of the money puts would be higher than Black Scholes (which uses a historical volatility in the middle of the smile) would obtain. In addition, in-the-money calls (strike/spot less than one) will be less expensive than Black Scholes, because volatility decreases as strike/spot increases (as calls move towards at-the-money). Basically, this seems to mean that the market thinks that, as puts move more out of the money, they are more likely to be able to make a large move back into the money. Conversely, as calls move towards at-the-money, they are less likely to make a large move back into-the-money. This does not make much sense to me. Wouldn't a higher volatility as the call moves more into the money give it a higher price? Perhaps the slope of the curve as the option moves out of the money is what is considered important (ie hedge against losses). If an out-of-the-money put's strike/spot ratio decreases (more out-of-money), volatility rises. As an in-the-money (left of smile) call's strike/spot ratio rises (moving toward at-the-money), volatility declines.
This phenomenon is known as volatility skew. I am unsure whether the same price discrepancy applies to the right side of the smile (i.e. out-of-the money calls overpriced and in-the-money puts undervalued vs. Black-Scholes).
The point of such computation is to show that a different volatility model may facilitate better pricing. One such model is stochastic volatility (volatility for a given time and underlying price follows a probability distribution). One stochastic process is mean reversion (volatility moves up and down around a mean).