Vega vanna volga models seem to be popular is 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 in the equity, futures, or commodity derivatives markets. If not, why? What makes the model suited specifically to FX markets?


FX differs from other asset classes in that certain amount of market manupulation by cebtral 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 the 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. In order 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.)

  • $\begingroup$ By asymmetry due to 'missing the opportunity to make money by buying a call' do you mean OTM calls are in less demand so the implied distribution has a less fat tail at higher strikes- or that the OTM call buyers are okay with making less money by paying a higher premium- or something else? (Sorry the wording of your post is a bit confusing). Thanks! $\endgroup$
    – Slade
    Oct 21 '19 at 1:23
  • $\begingroup$ I think asymmetry can exist in equity markets due to structural reasons. For example if you incorporate a probability of default into your model then it will generate a smile. I understand what vega vanna and volga are; I don’t understand how your description of central bank intervention necessitates such a framework or why it would invalidate such a framework in the case of equities. $\endgroup$
    – roz
    Oct 21 '19 at 3:25
  • $\begingroup$ And anyway, I am not even sure about your claim that someone would not intervene if equity prices went too low. Central banks have done so in the past havent they? Quantitative easing and zero interest rate policy are examples of monetary policy enacted by central banks to boost asset prices they deemed too low. $\endgroup$
    – roz
    Oct 21 '19 at 3:27

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