Question

If the Black model is correct, what should be the relation between the strike price on options on a futures contract (such as on natural gas future) and the volatilities implied by the prices of these options? What relation between strike and implied volatility is typically observed in reality? Provide a brief explanation of what can account for the observed strike-implied volatility relation. Why might the “smile” “smirk” towards the “call wing”? Why might it “smirk” towards the put wing?

Looking to get some help on this question. Thanks

Answer 1

Implied volatility is an important aspect of the time value premium of an option. As implied volatility increases, call and put option prices go up. When implied volatility decreases, option prices go down.

Implied volatility is a concept specific to options and is a prediction made by market participants of the degree to which underlying securities move in the future. Implied volatility, essentially, is the real-time estimation of an asset’s price as it trades. This provides the predicted volatility of an option’s underlying asset over the entire lifespan of the option, using formulas that measure option market expectations. When option markets experience a downtrend, implied volatility generally increases. Conversely, market uptrends usually cause implied volatility to fall. Higher implied volatility indicates that greater option price movement is expected in the future.

The Black Scholes model actually assumes that volatility is constant. As a result the IV should be a flat line. But what actually happens is that, in case of stocks, as the stock price falls , investor activity increases because its a negative event. And therefore volatility increases. That is why the smile for equities is like a smirk, downward sloping. This implies that at lower prices with respect to the strike price, there will be a higher volatility.

In case of commodities, an increase in prices is a negative event. Therefore an increase in the underlying price increases volatility and therefore that smile would be upward sloping. and so at prices higher than the strike price, there is higher volatility.

For something like forex, stability is very important. That is why an appreciation or depreciation both lead to volatility. And that is why the IV curves up in both the directions. Volatility increases if the rate shifts either way.