Hawkes processes for modeling event arrivals on the intraday market for electricity deliveries in Germany and their use in optimal market maker pricing

Market making is a trading strategy on markets with continuous trading which essentially involves enabling other market participants to buy and sell at the market. A market maker needs to decide how much money she requests for selling and how much money she is willing pay for buying. The intraday market for electricity deliveries in Germany has continuous trading in place. This thesis is devoted to the question how a market maker on that market could find her sell and buy prices.

The thesis has four parts. The first part is devoted to fundemental aspects of the question under consideration. In the second part different models for how buys and sells arrive in the market are discussed. In the third part a time series model for some of the parameters of the model from the second part is developed and analyzed. The fourth parth is then about a model for the activity of a market maker which yields the prices at which she should offer to sell and buy. The main findings in the last three parts are summarized in the following.

One contribution of the second part is empirical evidence for greater intensity of market order arrivals close to gate closure and clustering in market order arrivals. Building on these observations, we address the question whether the Hawkes process is suited to model the clustering. We leave the question whether other models which result in clustering of market order arrivals may also be suited to future research. The same holds true for the assessment which clustering model outperforms the other. The goodness-of-fit of the Hawkes process turns out to be clearly better compared to the same model without excitation. On that basis, we identify some characteristics of the estimated Hawkes processes for each contract. Examples are a strong but short-lived self-excitation, more offspring due to market orders on the same market side than on the other market side, and a strongly negative relationship between the time-zero level of the exponential growth component of the baseline intensity and its growth rate.

In the third part, we develop an individual additive model for the intensity parameters for each market side which consists of a level, an intra-day periodicity and a stochastic component. Concerning the periodicity, a dummy-variable model and a polynomial model perform similarly as opposed to a truncated Fourier series model. All three models underestimate the periodicity in the branching ratio, a quotient which is related to the average number of arrivals due to self-excitation. We model the stochastic component with a vector-autoregressive model and focus on auto-correlation in the error in choosing the number of lags. A comparison of the forecast performance of our model with two benchmarks (zero conditional expecetion, random walk) reveals that it largely outperforms the other two.

In the fourth part we find that the optimal depths of the market maker depend negatively on the current bid-ask spread: the larger it is, the closer she will post her limit orders to the best buy and sell limit order. If the dynamics of the bid-ask spread change such that that it is expected to widen more, the market maker is less aggressive once she has built up a position and the end of her trading window is still far away. Her penalty on inventory held during her window of activity is negatively and non-linearly related to time. The relationship between her penalty on inventory held at the end of that window and time is positive and also non-linear. The impact of self-excitation in the arrival rates of market orders causes the market maker to decrease her aggressiveness on the respective market side and to increase it on the opposite market side. The performance assessment of the strategy reveals that it clearly outperforms a naive market making strategy. The performance of the strategy which involves excitation in event arrival rates exceeds that of the strategy without excitation by a small amount at most. The strategy which involves the solution without approximations of the fill probabilities tends to outperform the strategy with linearly approximated fill probabilities, even though there are combinations of the inventory penalties which cause this relation to be reversed.


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