How Return Skew Affects Black–Scholes Option Prices
Summary
The document asks how a positively skewed stock-price distribution affects Black–Scholes–Merton option valuations across strikes. It includes two brief responses: one links right-skewed outcomes to greater probability of high terminal prices and a higher value for out-of-the-money calls; the other discusses volatility differences across strikes and suggests that a constant-volatility model can misprice options. Together, the responses point toward distribution shape and the volatility smile or skew as relevant considerations in option pricing.
The explanations are incomplete and do not establish a consistent pricing conclusion for every moneyness category. One response contains a directionally confusing statement about lower volatility and higher option prices, while the other focuses on exercise probability without quantifying payoffs or risk-neutral probabilities. The document offers no derivation, market data, or calibrated comparison. Its claims should therefore be treated as an informal starting point: skew can affect option values, but pricing requires specifying the return distribution and valuation measure, rather than inferring prices from exercise probability alone.
Key ideas
- A positively skewed stock-price distribution assigns more weight to high-price outcomes.
- The responses suggest that skew can affect the values of options at different strikes.
- A constant-volatility Black–Scholes–Merton model may not capture strike-dependent implied volatility.
- The explanations are informal and do not provide a complete or internally consistent pricing derivation.
Tags
Full text
# Black-Scholes-Merton formula and option pricing # Black-Scholes-Merton formula and option pricing If the distribution is skewed to the right,Black-Scholes overprices out-of-the-money puts and in-the-money calls. It underprices in-the-money puts and out-of-the-money calls. How? Stock price log-returns distribution is skewed to the right means it is a log-normal distribution. I know the moments of log-normal distribution and how it relates to normal distribution. But how does Black-Scholes-Merton formula overprice out-of-the money puts and in-the-money calls and underprice in-the-money puts and out-of-the money calls? It is just because of volatility of option prices at different strike prices or any other reason? ## Answer by Winodd Dhamnekar (score 2, accepted) https://quant.stackexchange.com/a/48673 I am giving answer to my question. If the stock price log returns distribution is skewed to the right, then $mode<median<mean$ in most of the cases. The strike price of an OTM calls lies to the right of the current price. So the demand for an Out of the money calls are low as the probability that they will turn into an In the money calls is less. As a result, volatility is lower than Black-Scholes-Merton formula assumption. So, their prices will go up. But BSM formula assumes constant volatility. So it underprice an Out of the money calls and In the money puts. ## Answer by Kevin (score 3) https://quant.stackexchange.com/a/47488 Suppose the distribution of the stock price $S_t$ is positively skewed and thus, assigns more weight (higher probability) to outcomes with high stock prices. The exercise price of an OTM call lies to the right of the current price and thus, the exercise probability increases noticeably which results in a higher option price.
Shown in full with attribution under the source's licence. Licence: CC BY-SA 4.0 (Stack Exchange)
This summary was written by Stratmill's research agent from the original; it is not a copy of the source.