Why Vega-Vanna-Volga Pricing Is Associated With FX Options

# Are Vega-Vanna-Volga methods/models also used in equity derivatives? Or only in FX? Why?


# Are Vega-Vanna-Volga methods/models also used in equity derivatives? Or only in FX? Why?












Vega-Vanna-Volga models seem to be popular in the FX derivatives market and are often calibrated via 25 delta risk reversal, Vega weighted butterfly, and ATM straddle quotes. I am wondering if they are also used to price equity and commodity derivatives. Is there something that makes the model particularly suited to FX markets?

## Answer by Dimitri Vulis (score 3)

https://quant.stackexchange.com/a/49280

FX differs from other asset classes in that some market manipulation by central banks is the norm. For almost any currency, if its exchange rate versus other currencies moves outside a certain band, the central banks will try to intervene, usually by just buying the currency in the market. The bank's goal is not to make money by speculation, but to keep the exchange rate within this band. The resources that the bank spends on the intervention are likely to end up the P&L of some other market participant whose goal is to generate P&L. If a currency hovers near one side of the band, then the intervention from that side is more likely than from the other. This is the fundamental reason for the asymmetry and for the importance of the risk reversal.

Because of these complicated dynamics, when you price FX exotic options, you estimate the "overhedge" - the additional cost of hedging the volatility risk, and include it in the price of the exotic. The vanna $\frac{d\ vega}{d\ spot}$ is simply the change in vega due to change in spot. The volga $\frac{d\ vega}{d\ vol}$ is the change in vega due to change of volatility. If they are non-zero, then every time the spot or the vol changes, your vega changes. To keep your vega exposure flat, you must trade some vanilla options.

No comparable market intervention happens in equities. There still are fat tails because (main reason among many) for almost any equity, there are many outstanding limit orders to buy/sell if the price goes above/below some threshold, which is usually a round number. There is some asymmetry because (one important reason among many) psychologically for many people losing money (by selling a put) is more painful than missing the opportunity to make money by buying a call. But I can't imagine a situation where, if an equity price becomes "too low", someone would intervene and spend lots of money not in the hopes of making money, but just to keep the price up. (If the price appears too low and the company has the requisite cash, it may engage in shares buy-back, but that's a very slow process and does not affect the price much.)