Volga
Second derivative of price vs. volatility
What is Volga?
Volga Volga is the second derivative of an option's price with respect to implied volatility, measuring how an option's vega changes as volatility moves. Also known as vomma or vega convexity, volga captures the non-linear relationship between option value and implied volatility. The term "volga" is particularly prevalent in foreign exchange (FX) options markets, where it plays a central role in pricing and risk management. How it works: Vega measures the linear sensitivity of an option to volatility changes, but vega itself is not constant. Volga measures this second-order effect: how much vega increases or decreases as IV moves. Options with high positive volga benefit from large volatility moves in either direction because their vega grows as IV rises. At-the-money options have near-zero volga because their vega is at its peak and relatively stable. The highest volga occurs in out-of-the-money options where vega is small but highly sensitive to IV changes. For example, in FX markets, a 25-delta risk reversal on EUR/USD might be priced using the ATM volatility, the 25-delta butterfly (which captures volga), and the 25-delta risk reversal (which captures skew). A 25-delta strangle has high volga because both wings are OTM. If EUR/USD implied volatility jumps from 8% to 12%, the strangle gains more than a simple vega calculation would suggest because volga adds convexity profit. The vega on each leg increases as IV rises, creating an accelerating gain. In equity markets, volga explains why far out-of-the-money options are often priced above their Black-Scholes theoretical value. Market makers add a volga premium because they know that in a crisis, the vega on OTM puts will explode, creating outsized losses for the seller. This volga premium is one of the key factors driving the volatility smile. Understanding volga helps traders evaluate whether the premium paid for OTM options is justified by their convexity benefits.
Complete Definition
Volga is the second derivative of an option's price with respect to implied volatility, measuring how an option's vega changes as volatility moves. Also known as vomma or vega convexity, volga captures the non-linear relationship between option value and implied volatility. The term "volga" is particularly prevalent in foreign exchange (FX) options markets, where it plays a central role in pricing and risk management. How it works: Vega measures the linear sensitivity of an option to volatility changes, but vega itself is not constant. Volga measures this second-order effect: how much vega increases or decreases as IV moves. Options with high positive volga benefit from large volatility moves in either direction because their vega grows as IV rises. At-the-money options have near-zero volga because their vega is at its peak and relatively stable. The highest volga occurs in out-of-the-money options where vega is small but highly sensitive to IV changes. For example, in FX markets, a 25-delta risk reversal on EUR/USD might be priced using the ATM volatility, the 25-delta butterfly (which captures volga), and the 25-delta risk reversal (which captures skew). A 25-delta strangle has high volga because both wings are OTM. If EUR/USD implied volatility jumps from 8% to 12%, the strangle gains more than a simple vega calculation would suggest because volga adds convexity profit. The vega on each leg increases as IV rises, creating an accelerating gain. In equity markets, volga explains why far out-of-the-money options are often priced above their Black-Scholes theoretical value. Market makers add a volga premium because they know that in a crisis, the vega on OTM puts will explode, creating outsized losses for the seller. This volga premium is one of the key factors driving the volatility smile. Understanding volga helps traders evaluate whether the premium paid for OTM options is justified by their convexity benefits.
Related Terms
Frequently Asked Questions
What is Volga in options?
Volga is the second derivative of option price with respect to implied volatility, measuring how vega changes as IV moves. Also called vomma, it captures the convexity of option value relative to volatility. High volga means the option gains value at an accelerating rate during large volatility moves.
How is Volga used in FX options markets?
In FX options, volga is a core pricing input alongside ATM vol and risk reversal. The 25-delta butterfly spread directly isolates volga exposure. FX market makers quote butterfly spreads as a way to trade volga, and the volga level helps determine the curvature of the volatility smile across delta space.
Why does Volga matter for the volatility smile?
Volga explains why OTM options trade at higher implied volatilities than ATM options. Sellers of OTM options face convexity risk from volga: if IV spikes, the vega on OTM options grows rapidly, creating larger losses. To compensate, sellers charge a volga premium, which inflates the IV of OTM options and creates the characteristic smile shape.
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