# How to Explain Implied Volatility Surface Skew by Option Market Supply and Demand?

Skew in the implied volatility surface usually means the implied volatility is negatively correlated to option strike. We can explain through many angles:

- leverage effect: when the stock price drops, the company has a greater leverage ratio, hence a greater volatility
- spot-vol correlation effect: volatility process is negative correlated with stock price process
- jump effect: big jumps tend to be down than up
- risk of default: there is positive probability company default
- bucket correlation: when stocks drop, the correlation between stocks increases, and when stocks grow, the correlation gets smaller. A high correlation between individual stock results in greater volatility
- volatility is empirically log-normal distributed

We can also explain skew through supply and demand. Let’s review the market for vanilla options, called flow derivatives.

The demand for an index put option is about ten times more than call options, and index options demand is much greater than single stock options. A detailed data analysis can be found in this paper. [1]

Let us assume you are a portfolio manager at BlackRock, and your holding is very closed to SPX. You are given an order from clients; if your portfolio drawdown is greater than 10%, you will be fired. Then the best way to protect you is to purchase a 10% out-the-money put option. In this situation, you will never have a 10% drawdown if you do not consider option premium. But what if you do not want to pay put option premium? You sell out-the-money call index options and single stock options. It is a covered sell; you limit your drawdown (reduce your tail risk) by sacrificing some positive exposure profits.

This activity and motivation domain the flow derivative market, and it is why people regard options as insurance. Why is the trading volume of call options used as insurance not as high as to put options? Because there are many cheaper ways to increase leverage for positive exposures, like buying stocks using a margin account. Shorting sale is always harder than buying stocks, and it is one reason the put option is popular.

Big buy-side firm long out-the-money put and short out-the-money call increasing the volatility of put wing and reduce the volatility of call wing, which increases the volatility skew. Because of put-call parity, implied volatility for call and put at the same strike should be the same (not the same but close if we consider transaction cost of arbitrage strategy). Then the in-the-money call option implied volatility is driven by the out-the-money put and put-call parity.

So in the big view, the principal consumer of the flow derivative market is big buy-side firms, who want to pay some returns to purchase tail risk insurances. Then market makers provide liquidity, and the pop trader provides information, sharing the insurance fee of big buy-side and taking the corresponding risks.

We can try to build some alpha research ideas based on this market structure. We can use implied volatility skew to predict the underlying price. If the implied skew gets greater, meaning more portfolios managers worry about drawdown, we bet the underlying will drop and vice versa. Second, we can use the difference between the demand for put and the demand for call options to predict the underlying price. Those two strategies can be found in this paper. [2]

Reference:

[1] Garleanu, Nicolae, Lasse Heje Pedersen, and Allen M. Poteshman. “Demand-based option pricing.” *The Review of Financial Studies* 22.10 (2008): 4259–4299.

[2] Jin, Wen, Joshua Livnat, and Yuan Zhang. “Option prices leading equity prices: Do option traders have an information advantage?.” *Journal of Accounting Research* 50.2 (2012): 401–432.