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Vanna–Volga pricing - Wikipedia


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Cancel Vanna is a greatly under-used, higher-order option tool. Apart from being useful in its own right by virtue of its plain definition, it is also a valuable indicator that reveals information about the structure of an option portfolio, as well as the dynamic properties of a portfolio with respect to time. It remains, however, conspicuous by its absence from many traders' and risk managers' typical risk profile matrices. This Learning Curve aims to explain the advantages of vanna and combining it with vomma, another higher-order option.

Understanding VannaVanna is typically defined as the change in option delta for a change in implied volatility. Call options have positive vanna, and puts have negative vanna. This is because an increase in implied volatility raises the chance that any call or put will expire in-the-money and this is synonymous with a higher, absolute delta. Perhaps a principle reason for the lack of attention vanna receives is that the risk associated with it might be thought innocuous. After all, hedging the effects of vanna is simply a matter of hedging with the spot product.

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As implied volatility changes, the portfolio delta changes due to the eueope vanna and the trader simply neutralizes the effect by buying or selling the underlying product in the relevant quantity. This opfion is however an euroe and also omits vanna's other potential uses. Firstly, being a higher-order Greek, its potency is often magnified by compound events. Let's take an example of a portfolio that is long calls, short puts, fully delta-hedged and vega neutral. This position will exhibit positive vanna, as both the long calls and short puts are vanna positive. Now, if the spot price is unchanged, it is true to say that the trader is not greatly concerned by her long vanna exposure.

Now, however, consider two concurrent events; namely the implied volatility increases and the spot price falls.

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In this case, the trader is running into eurole short put position as implied volatility is rising, which is unfortunate. The trader is long vanna; the implied volatility is rising, so the delta position increases. This is where you have double trouble. In short, vanna is a greater risk when multiple events occur. In this sense, it is a complex risk ideally suited to situations when a trader's own outlook is more specific with respect to the covariance of an underlying's price and implied volatility movement. When using hedged options to form a certain strategy, or to structure a desired pay-off profile with respect to the spot price and implied volatility, vanna effects should always be included in the calculation.

Using VannaThe uses of vanna however go well beyond those implied by its simple definition.

A secondary use of the vanna metric is as an indicator of the portfolio's vega profile with respect to the upside and downside. In complex inventories containing longs and shorts of varying strike and quantities, vanna provides a single number that can at least in part summarize the distribution of option premium across the curve. So an array of longs and shorts can be simplified by taking the weighted average vega contributed by the inventory in each strike. The outcome may be a conclusion that, on balance, the portfolio is long calls upside and short puts downside.

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Another way to achieve the same goal would be to view the vega risk up and down on eugope underlying price-slide risk matrix. But in many cases, both methods can be approximated by a glance at the vanna metric. By definition, positive vanna implies a position that is either net long calls, net short puts or both. The usefulness of this shortcut can be augmented in two ways.

Vanna–Volga pricing

Firstly, by having in mind the vanna of a certain option or options, the position can be synthetically converted into a vanna-equivalent position. Having these numbers memorized or otherwise to hand, can certainly pay dividends in fast markets or when inventories become highly complex. In earlier chapters we have seen: We used implied volatility surfaces to plot the behaviour of volatility across these two dimensions. As part of this exploration process we will introduce the concept of Shadow Gamma and Vanna — both instances of what we could call cross Greeks. Since by now we have spent sufficient time with the concept of surface plots, we will also add a new dimension, the underlying asset price, to our surface plots.

Calculating Vega The equation for calculating Vega is given by: Since assume no dividends, the formula simplifies to: We can use either of the two equations to calculate Vega. Similar to Gamma, the value of Vega is the same for both call and put options.

erope Volga — Volatility Gamma Volga or Volatility Gamma determines the rate of change in Vega on account of a unit change in volatility. The same relationship convexity has with duration and gamma has with delta. It is also possible to express both Vanna and Volga in terms of Vega. We know that Vega is given by: Unlike Gamma where Gamma peaks with a reduction in time for at the money option, for Vega, Volga and Vanna, it is increasing time that give volatility an opportunity to impact option value. The Vega Greeks will decline as time to expiry comes closer to zero.


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