It’s all about Optimal Timing!

Updated: Jun 28, 2021

As we explained in our previous article on Gamma-Hedging (if you missed it, you can find it here), one of the challenges of risk hedging is to choose the right time to Gamma hedge the hedging portfolio. Indeed, this portfolio needs to be rebalanced frequently enough to be well hedged, but not too frequently to avoid paying too many transaction fees. So, it’s all about right timing!

At Kesitys, we have been working on this issue for many years and have developed a solution that is both efficient and easy to use: TEMPO Gamma-Hedging.

A new Gamma hedging strategy

TEMPO Gamma-Hedging is a decision-support tool that helps traders hedge their portfolio at the right time. TEMPO follows the risk evolution of a benchmark strategy provided by its user and, when fed real-time market and portfolio data, sends intervention signals that minimize trading costs.

Let’s see its effectiveness on an example.

To keep it simple, we first show an example on a portfolio consisting of a single European Call Option on a simulated market. We set TEMPO to follow the risk evolution of a Close-to-Close hedging portfolio (that is rebalanced every day at market close).

We monitor the evolution of this portfolio over 1 month (depicted in red below).

  • The evolution of the Close-to-Close hedging portfolio, which is rebalanced 20 times, is depicted in yellow.

  • The evolution of the hedging portfolio that follows the rebalancing signals provided by TEMPO is depicted in blue. This portfolio was rebalanced only 5 times during the same period. By rebalancing less often but more efficiently, its transaction costs were reduced by 43%.

The risk level of both portfolios is measured by the realized variance of the book P&Ls; we can see that the levels of both strategies are similar throughout the simulation.

TEMPO follows the same risk profile as its reference strategy.

Features of TEMPO

TEMPO is the result of 4 years of research and development and is based on innovative and advanced tools from stochastic dynamic programming, statistical learning and time series analysis.


  • Data-driven: no pricing or data model is used to compute the signals, only market data and the portfolio greeks.

  • Portfolio-driven: TEMPO adapts its signals in real-time to the evolution of its user’s portfolio.

  • Statistically optimal: the optimality of the signals is mathematically proven.


Did you know? In a Black-Scholes model, we have proved that TEMPO reduces transaction costs by at least 27% compared to the Close-to-Close strategy, for the same risk level.


Track records

TEMPO Gamma-Hedging has already proved its effectiveness on real equity & index portfolios.

Track record 1: >15 portfolios of vanilla options

Characteristics of the use-case:

  • TEMPO was compared with the Close-to-Close strategy, which was the one used by the trading desks.

  • The risk measure that was chosen by the traders was the realized variance of their P&L.

On these portfolios during a 6-months test:

  • The trading costs were reduced by an average of 33%.

  • The risk constraint was respected: the ratio of P&L realized variances between TEMPO and the original strategy was at 1.1.

  • The number of rebalancing signals was reduced by over 70%.

Track record 2: a Société Générale index portfolio

Characteristics of the use-case:

  • TEMPO was compared with two strategies: the Close-to-Close strategy and a Threshold strategy on residual Delta (cf details below).

  • The risk measure was the realized variance of the P&L.

  • A backtest was performed on 2017 and 2018 data.

Details on the Threshold strategy:

Residual Delta: Delta of the global trading book (options portfolio + hedging portfolio). If the book is perfectly Delta hedged, then the residual Delta is zero.

Strategy: when the residual Delta reaches a certain threshold X, a rebalancing signal is triggered.

Choice of the threshold X: in order to compare all three strategies, the threshold was computed ex-post so that the Close-to-Close and Threshold strategies would have the same risk levels in 2017. The threshold X determined for 2017 was reused in 2018.

Results for 2017 :

Over the year, while keeping roughly the same level of risk as the Close-to-Close strategy, TEMPO reduced transaction costs by 40% and the Threshold Delta strategy reduced them by only 24%.

Results for 2018 :

In the results above, two elements are important to note:

  • The threshold computed in 2017 to maintain the same level of risk as the Close-to-Close strategy is no longer valid for 2018 and the risk level decreased by 40%, while the trading costs increased by more than 50%. This shows how difficult it is to choose such a threshold and to update it according to the market.

  • Over the year, and without changing any parameters compared to 2017, TEMPO reduced transaction costs by 15%.

A plug-and-play API

TEMPO is fully automated and easy to install and use. The software was implemented in C# on the NET platform, which allows a simplified installation on any type of machine (Windows, Mac, Linux, Cloud...). It is deployed at the trader’s premises as a RESTful API that follows the OpenAPI specification.

All that is needed is to connect the tool to the Portfolio Management System (PMS) and market data stream for it to deliver rebalancing signals at the frequency requested by the trader.


To sum up, TEMPO is a new Gamma hedging strategy that is:

  • Automated and statistically optimal

  • Data-Driven

  • Plug-and-Play

If you would like to find out more about TEMPO or test it on your own portfolios, write to us at


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