Vanna or dVega/dSpot or dDelta/dVol is a derivative of option vega with respect to the price of the underlying asset, which is equivalent to a derivative of the delta with respect to volatility. According to the laws of mathematics, it also indicates the sensitivity of the option delta to changes in implied volatility.
According to Black-Scholes model assumptions, all options with different strikes and exercise dates have the same implied volatility, i.e. implied volatility does not depend on either the option's moneyness or the expiry date.
Option’s speed measures the change in gamma with respect to the change in price of the underlying asset, all other things being equal. Mathematically, a dGamma/dSpot is the 1st derivative of the gamma of the price of the underlying asset or a 3rd order derivative of the price of an option with respect to the price of the underlying asset.
The time structure graph depicts implied volatility of options with the same strikes but different expiry dates. As a rule, traders look at at-the-money options to plot the term structure. At the same time, drawing the term structure from OTM options can also provide very useful information.
If the current form of the time structure of volatility does not reflect a trader's point of view, then the trader can use this opportunity to trade options. The term structure is traded via two similar strategies described in the section on volatility skew trading:
The option's Charm indicates how the option's delta will change as one trading day passes. Mathematically, the charm is a derivative of the delta with respect to time.
Vomma (also known as weezu or Volga) - indicates the change in an option's vega when the implied volatility changes by 1%. Vomma is a 2nd order derivative. This means that Vomma indicates how another option's greek changes, not the value of the option itself.
The formula for the approximate value of at-the-money straddle gives a fairly accurate estimate of the market price, taking into account the spot share price, implied volatility and the time to expiry.
Investors can trade volatility skew two ways
For simplicity, this article will consider implied volatility of options with expiry dates in 3 months and 12 months.