Modelling the real world can never be perfect, but there are ways to create something that’s as close to reality as possible. How do you know that it’s working? Alexandre Antonov, Director at Standard Chartered Bank, shares his method which involves recalibration, but there is a risk associated with that, according to Bruno Dupire, Head of Quantitative Research, Bloomberg.
What’s the best way to monitor the performance of futures, options and volatility and which metrics are the best?
Alexandre Antonov, Director at Standard Chartered Bank set out to answer this question as he presented his latest work on quantifying model performance at QuantMinds International in Vienna.
“There are known issues with models,” Antonov told the audience. “The model cannot automatically capture the changing market conditions.”
Current methodologies in use give little information about the model performance, making it hard to differentiate between the various options and hard to choose which one to use. The answer, he said, is to recalibrate, and come up with a metric that can classify different hedging strategies.
Antonov’s approach addresses the issue with a so-called replication portfolio which reproduces a payoff for all future scenarios from today to maturity. One of the ways it works is by looking at the trade backward, starting from the final value of the portfolio.
“If the hedge is not perfect, the payoff price is an average over the replicating portfolio,” he said.
Numerical experiments followed to test his work, using a real-world model, like Heston with typical parameters for principle currency pairs, to consider a European option with a 3-year maturity, calculating the defects of a set of hedging strategies and comparing the distribution of those defects.
“We have observed the Heston defect distribution having smaller mean and variance,” he said. “The Heston hedge is better than the others in a statistical way.”
Antonov walked the audience through a range of real-life examples, showing how he repeated his testing using real market data. While his findings show that the Heston model outperforms simpler models, like Black-Scholes, his methodology worked.
Even so, in general, “the most sophisticated models do not necessarily give better hedges,” he said.
Bloomberg’s Head of Quantitative Research, Bruno Dupire, warned about the dangers of recalibration.
“Can you build a model today that will successfully predict tomorrow?” he asked. “What we know is that we have thousands of stocks each one with lots of options. The need for automation means parametric forms are used and the parameters are frequently adjusted.”
Dupire looked at many examples, including those in the swaption market, and highlighted the logical and practical challenges that come up when the parameters move every day and the market constantly recalibrates.
He also looked at the example of the S&P skew and asked whether it is “safe” to recalibrate Black-Scholes, LVM, Heston and SABR. Parametrisation is pervasive in the market, he said, due to the need for automation, the different risk management scenarios and the fashion for Markov models.
“The problem is that there are very strong consistency conditions and several very popular models violate them,” he concluded. “So be very careful!”
Understanding how your model is performing in a quantitative manner is not easy, Alexandre Antonov, Director at Standard Chartered Bank, told us at QuantMinds International.