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Precious Metal Implied Volatility Precious metals are trading commodities. But a precious metal quote is very similar to a Forex quote. The quote is represented in the same way as a quote for a currency pair. For instance, the spot gold traded against the US dollar is XAU/USD. An implied volatility is the volatility implied by the market price of an option based on the Black-Scholes option pricing model. A volatility surface is derived from quoted volatilities that provides a way to interpolate an implied volatility at any strike and maturity. Unlike in other markets that quote volatility versus strike directly, the precious metal or FX smile is given implicitly as a set of restrictions implied by market instruments and as such a calibration procedure to construct a volatility- delta or volatility-strike smile is used. In the past, precious metals were the foremost commodity-based form of payments. The use of precious metals as currency led to the production of coinage that was used as trading devices. The institution of coinage further led to the development of representative currencies in the form of notes. Later on, major world currencies were pegged to the value of gold. After the collapse of the Breton Woods agreement, precious metals are no longer used as a primary mode of monetary transactions. But they continuous to share a close relationship with established currencies. A precious metal quote is very similar to a Forex quote. The quote is represented in the same way as a quote for a currency pair. For instance, the spot gold traded against the US dollar is XAU/USD. Spot precious metal prices are quoted in USD per troy ounce. Thus, a quote of XAU/USD 1000 means 10z of gold is equal to $1000 USD. Therefore, precious metal volatility smile is represented by three entities: at-the-money (ATM) volatility, risk reversal, and butterfly. The standard market quotes are ATM level, 10 delta risk reversal, 10 delta butterfly, 25 delta risk reversal, and 25 delta butterfly. The ATM volatilities quoted by brokers can have various interpretations depending on currency pairs. Here we introduced the most popular one used by the FX brokers. The ATM volatility is the value from the smile curve where the strike is such that the delta of the call equals, in absolute value, that of the put (this strike is called ATM “straddle” or ATM “delta neutral”). A risk reversal (RR) is a combination of a long call option and a short put option with the same maturity. This is a zero-cost product as one can finance a call option by selling a put option. Risk reversal volatility is the difference between the volatility of the call option and the put option at the same moneyness level A butterfly (BF) is a combination of a long call option, a long put option, a short ATM call option, and a short ATM put option. Butterfly volatility is the average of the difference between the volatility of the call option and put option minus the ATM volatility Reference |