Over the last two decades the research field of quantitative finance has become a vibrant field of academic research and an indespensible tool for financial decision making. Berlin researchers have made significant contributions to many areas of quantitative finance. Our areas of expertise include:

Cross Hedging of Financial RiskReducing or even eliminating a particular risk is an important task in risk management. However, often only imperfect hedging instruments are at hand, leading to basis risk. A prominent example is an option on a stock market index. In practice such options are often hedged using index futures. 

Dark Markets and Hidden Liquidity. There is considerable empirical evidence that suggests that order exposure in limit-order markets can increase, while shielding ones trading interests from public view can substantially decrease transaction costs. More and more securities markets are thus providing hidden liquidity as a strategic trade-tool to investors, either by virtue of “dark” exchanges with limited/zero pre-trade transparency like Dark Pools or by introducing  Iceberg Orders on traditional exchanges.

Econometric Tools for High Frequency Data. Methods and models for high-frequency data are of growing importance in financial practice. Important tasks are high-frequency predictions of trading volumes, market depth, bid-ask spreads and trading costs to optimize order placement and order execution. Berlin researchers made significant contributions in this area.

Financial Modelling with Affine Processes. The practical need for tractable mathematical models for incomplete financial markets has spurred a lot of interest in the class of affine processes. In the realm of equity and interest rates, models based on affine processes have been proposed to accommodate stochastic volatility, jumps in asset prices, time-varying intensity of jump risk, as well as self-excitement and cross-excitement phenomena between economic factors.

Hedging in Illiquid Markets. Hedging financial risk is one of the key tasks in investment banking and requires sophisticated mathematical methods to be carried out systematically and efficiently. Most models used for this purpose, however, disregard that hedging strategies themselves may move prices when markets are not perfectly liquid and thus may fail to include liquidity risk when computing prices and hedge ratios. 

Implied and Stochastic Volatility. Volatility is a multifaced key concept of modern finance, its importance being acknowledged from both academics and industry practioners; the recent activity in the field exhibits remarkable mathematical depth and makes uses of various aspects of asymptotic (stochastic) analysis as well as (linear and non-linear viscosity) PDE methods. 

Interest Rate Modeling and Pricing of Structured Callable Products. Modelling the term structure of interest rates has long been a focus of reserach in Berlin, especially at the Weierstraß Institute. A particular focus is on LIBOR models and on efficient numerical algorithms for the valuation of complex structured callable products.

LIOBOR Models. The LIBOR market model is favored by practitioners, however has certain well-know pitfalls. The random terms entering the drift are among the most important pitfalls, since exact closed-form pricing formulas cannot be derived and one has to resort to approximations, the “frozen drift” method being the most popular one. 

LOBSTER-Reconstructing Limit Order Books. In recent years electronic limit order book markets have become the dominant market structure for equity markets. Reconstructing order books is complex and challenging for many reasons. LOBSTER, our new limit order book reconstructuer provides an easy and flexible platform for reconstructing order books for reserach in quantitative finance and financial econometrics.

Optimal Order Placement. Any trading strategy is ultimately implemented by a stream of buy or sell orders. These orders are placed at trading venues whose liquidity varies over time, depending on the total flow of incoming orders. As a result, transactions affect market prices, typically in an adverse way. It thus becomes an issue how to optimally schedule the placement of single limit order market orders so as to trade-off their urgency against their costs, a challenging stochastic optimization problem to which Berlin researchers have contributed in a number of publications. 

Vast-Dimensional Asset Covariance Estimation. A challenging task is the estimation and prediction of covariance matrices covering potentially several hundreds of assets, as required, e.g., in portfolio management, risk management and asset pricing. Moreover, today’s practitioners often need to manage the risk of portfolio positions over comparably short horizons, such as, a day, a week or a month while requiring well conditioned and numerically stable covariance estimates.