Combo: hedge for less!

Updated: Jun 28, 2021

In our previous articles, we discussed some of the issues with Gamma hedging (here) and one of our solutions to optimize this process: TEMPO (there).

TEMPO provides traders with intraday signals to rebalance their hedging portfolios. But this may not work with traders who are constrained on their trading times. To fit the needs and constraints of such actors, we have developed another Gamma hedging solution: COMBO.


COMBO, just like TEMPO, aims at minimizing transaction costs. But COMBO works under an additional constraint: to perform rebalancing operations only at predefined times.


For example: COMBO is particularly suitable for derivatives traders who rebalance their

hedging portfolio every day at market close, either because they have a limited intraday market access, or because they wish to take advantage of the increased liquidity at that time.


The goal of COMBO is to provide hedging signals that minimize transaction costs while controlling the risk level of the hedging portfolio. More specifically, the tool is set up with a risk ratio X specified by the user and targets a risk-level increase of at most X compared to the Delta-Flat strategy.

At each rebalancing time, the tool is fed market data, the portfolio greeks and the current hedging portfolio composition, and does the following:

  1. First, it computes if the rebalancing is actually necessary.

  2. If so, it computes the new composition that the hedging portfolio should have.

Reminder: The Delta-Flat or Close-to-Close strategy is the strategy that consists in rebalancing the hedging portfolio every day at market close, in such a way that the residual delta is zero.

Obviously, the higher the risk traders are willing to take, the higher the percentage of transaction cost reduction.

Track records

Track record 1: S&P 500 options portfolio

A backtest was performed on a synthetic portfolio of options on the S&P 500 index, with market data from April 2018 to June 2019.

As can be seen on the following graph, the market was particularly hectic on some periods and Combo works well both with high and low volatility.


As can be viewed on the graphs below, the COMBO portfolio fulfils its hedging role well.

  • The risk ratio between P&L realized variances of the two strategies is 1.001

  • Trading costs were reduced by 24%

Note: Visible jumps are due to overnight S&P 500 jumps.

Track record 2: Société Générale European index portfolios

During our incubation at Société Générale Global Markets Incubator in 2020, we tested COMBO on several of their portfolios. This confirms that even under real conditions (market data and portfolios), COMBO delivers stable results.

Characteristics of the use-case:

  • The risk measure was the standard deviation of the daily P&L

  • A backtest was performed on 2017 and 2018 market data.

Features of Combo

COMBO is the optimal solution to a discrete-time stochastic control problem. Although based on distinct tools than TEMPO, this product retains several features that are important to us:

  • COMBO returns the optimal solution to the hedging problem. Statistically, for a chosen risk level, the induced strategy generates the least transaction costs.

  • COMBO is data-driven: only real-time data is needed, no training phase is required.

A ready-to-use technology

COMBO is delivered to the user as an API. It can be invoked from a thick client (a front-office application developed in C++, Java etc.), from a Python script, or even from VBA.

The inputs required by COMBO are standard:

  • Market data (spots, volatility).

  • Portfolio greeks.

  • Trader parameters (target risk ratio).

COMBO outputs the adjusted composition of the hedging portfolio, computed in order to minimize trading costs while targeting the given risk constraint.


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