Considering the size of UBS’s exotic derivatives books in Asia, it is not surprising the amount of attention the bank dedicates to this line of the business, while striving to stay ahead of the game.
When studying the riskiness embedded in exotic products, UBS’s management realised a competitive advantage could be gained with a better understanding of the volatility dynamics and its impact on their books, through a more accurate control of the Greeks, or risk sensitivities.
The Hong Kong-based quants and exotics traders collaborated to develop an application of local stochastic volatility (LSV) models to risk management and create a methodology to obtain stable Greeks.
Having stable and robust Greeks means the bank can better assess the profitability of a trade, detect in advance those trades that are potentially toxic, and spot possible mispricing of risk by other institutions. Ultimately, it allows the bank to hedge positions more efficiently and helps stabilise the P&L, as the profit on a trade can be locked in at inception.
“It allows us to be more selective in the business we want to do, and focus on the trades where we think there is more value for the firm,” says Fabien Falipou, head of equity index exotics and investment strategies trading for the Asia-Pacific region.
A problem the quant team had to solve was the inability of local volatility models to handle changes in future skew. Local volatility models the dynamics between spot price and volatility, but it fails to capture such dynamics when markets are under stress or when the volatility of volatility tops critical values.
Normally, spot changes are inversely correlated to volatility changes: when the spot price increases, volatility tends to decrease, and vice-versa. However, there are instances in which this pattern breaks down and correlation turns positive. The LV model is unable to capture the regime switch, and the values of delta and vega one obtains from it are wrong. The LSV model instead can account for the different correlation regime, and provides deltas and vegas that are more effective for risk management.
The standard practice in the industry for risk managing exotic books is to have a reserve, calculated with a SV model and often rebalanced monthly, and increased in case the market moves adversely. There is no predictive component in this approach, and therefore reserves are rarely hedged properly. “With our LSV approach, we have an actionable model and not just a theoretical one that gives you an amount of reserve,” says Falipou.
The introduction of the LSV models for risk management has been proved advantageous for many of the exotic products UBS works on, in particular autocallables and dual-corridor variance swaps. Dual-corridor variance swaps are considered natural hedges for autocallables. They are popular securities in Asian markets and are traded in large volumes, which makes their accurate risk management an important issue
The introduction of the LSV models for risk management has been proved advantageous for many of the exotic products UBS works on, in particular autocallables and dual-corridor variance swaps. Dual-corridor variance swaps are considered natural hedges for autocallables. They are popular securities in Asian markets and are traded in large volumes, which makes their accurate risk management an important issue.
Local stochastic volatility models are commonly used in banks for pricing derivatives and related valuation adjustments. In forex markets, they are used also for risk management purposes and there is a rich literature on them. In equity markets, however, quants and academics have developed LV models and SV models, but the application of the mixed model to risk management was uncharted territory until 2017. Modelling their dynamics, which entails taking dividends into account and estimating forward volatilities, poses some additional obstacles.
The difficulty is not in writing the model itself. That is relatively straightforward. Rather, “making the model practical and usable depends on how you calibrate it to the market,” says Vinay Srinivas, who heads the Asia-Pacific equity quant team for derivatives, Delta One and the quantitative analytics development group.
Srinivas’s Hong Kong-based equity derivatives quant team, in close collaboration with teams in other regions, develops many of the models on equity and exotics.
It is in the model calibration that the ingenuity of his team’s innovation shines. To calibrate the LSV model to observable market variables, Srinivas’s team resorts to two quantities. The first is the skew stickiness ratio (SSR), developed by Lorenzo Bergomi in 2009 and presented in Smile dynamics IV. The SSR gives a measure of the smile dynamics in the market: it is the expected change in at-the-money forward volatility relative to changes in the spot price. In other words, it quantifies the forward skew.
The second component of the calibration is the var-vol spread – the difference between the volatility swap per strike and the variance swap per strike. The var-vol spread gives a measure of the convexity of the skew.
“Matching LSV parameters to the market observed var-vol spread and to the dynamics of the volatility surface allows better application of the LVSV model for risk management” explains Alexandre Cohen, head of the equity derivatives quant team in Asia, who has worked on the expansion of the LSV model with his colleague Hao Zhang.
Srinivas and his team trust this can be a game changer, and expect other banks to adopt analogous solutions in managing the risk of exotic products.
Updates, September 13 and 14, 2018: After the publication of this article, Vinay Srinivas got in touch to clarify that he leads the Asia-Pacific, not the global, equity quant team for derivatives; that this team develops many, not the majority, of the models on equity and exotics, and that it does this in collaboration with teams in other regions. The article has been amended accordingly. The paragraph on local volatility and Alexandre Cohen’s comment have also been clarified.