Title: FX Options Market Sees Anomalous Volatilities in 2022, Leading Quants to Develop Innovative Solution
In 2022, the FX options market experienced abnormal volatilities, prompting quants to develop a groundbreaking solution. Yoshihiro Tawada, the head of FX-flow quant modelling at MUFG Securities EMEA, noticed a peculiar anomaly in the market for Turkish lira/yen options. During times of market turbulence, the mid volatility of these options breached the bid and ask boundaries, contradicting the assumptions behind pricing models and leaving them vulnerable to arbitrage strategies.
This anomaly arose due to a unique convention in the FX options market, where prices are quoted based on volatilities for specific deltas and expiry dates. Pricing screens typically display the volatilities for at-the-money (ATM) options, risk reversals, and butterfly structures. However, converting these values to obtain implied volatilities for bid and ask levels, from which strike rates are derived, can sometimes yield anomalous results, especially during periods of significant market movements.
Tawada sheds light on this issue, stating, Since the mid volatility is simply the midpoint between bid and ask volatilities, there is no guarantee that it will ensure an arbitrage-free order of strikes, even when the bid and ask quotes themselves are free from arbitrage. He further explains that when market volatility rises, and bid-ask spreads widen, mid volatilities become more prone to causing arbitrage. In extreme cases, the order of strikes may even reverse, leading to pricing discrepancies.
It is important to note that this phenomenon is not limited to lira/yen options; it can potentially occur with any currency pair. Tawada clarifies, As this is a matter of volatility level and smile shape, theoretically it can happen to any currency pairs.
Nonetheless, arbitrageable mid volatilities pose a significant challenge in pricing complex instruments, such as butterflies, that consist of out-of-the-money puts and calls. When strike orders are inconsistent, certain components of a butterfly will contradict the underlying assumptions, causing pricing models to malfunction.
To address this problem, Tawada devised a solution using variational inference, a machine learning technique that approximates probability distributions of latent variables. By optimizing the observable bid and ask values, the approach minimizes the disparity between the expected normal distribution of implied volatilities and the distribution that satisfies the no-arbitrage condition. This ensures that the derived mid volatility remains within theoretical boundaries, thereby guaranteeing an arbitrage-free implied volatility surface.
While the mathematical proof of Tawada’s solution may be complex, implementing it is relatively straightforward. Tawada affirms, The algorithm itself is not complicated since, apart from the arbitrage-free and strike-order consistency conditions, it involves minimizing quadratic functions.
Front-office quants who have reviewed Tawada’s paper appreciate the practicality of his solution. A senior quant analyst at a large European bank states, It’s a sensible solution to a practical problem traders have to deal with when they see inconsistent data coming from the market. Standard modeling usually assumes consistent data, but this algorithm aims to smooth out those outliers and create a more robust volatility surface.
Moreover, Tawada’s solution holds potential beyond the realm of FX options trading. It could be applied to mitigate arbitrage problems in other areas that experience volatility spikes. For instance, when measuring vega risk, traders typically bump volatilities and observe the resulting numerical difference, which can run into potential arbitrage issues. By accounting for such bumps in the no-arbitrage and strike-order conditions, the algorithm can help control boundaries and enhance market data in stressed scenarios.
In conclusion, Yoshihiro Tawada’s innovative solution to address anomalous volatilities in the FX options market showcases the power of variational inference and its potential applications. By minimizing inconsistencies and ensuring an arbitrage-free implied volatility surface, quants can better price complex instruments and minimize risks.
