THESIS
2016
xi, 69 pages : illustrations ; 30 cm
Abstract
In this thesis, we develop a high frequency market making strategy under a jump
diffusion process. In the past literatures, high frequency market making strategies are all developed under the assumption that the underlying asset follows a
diffusion process. However, in reality when a large size market buy (sell) order
arrives, it is of high probability that the mid price of the stock immediately jumps
to a higher (lower) value. To incorporate such impact of large size market orders,
we choose to use a jump diffusion process, which is a combination of a diffusion
process and a compound poisson process, to simulate the path of a stock's mid
price.
Based on the jump diffusion process that the underlying asset should follow, we
propose the Hamilton-Jacobi-Bellman equation by the kn...[
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In this thesis, we develop a high frequency market making strategy under a jump
diffusion process. In the past literatures, high frequency market making strategies are all developed under the assumption that the underlying asset follows a
diffusion process. However, in reality when a large size market buy (sell) order
arrives, it is of high probability that the mid price of the stock immediately jumps
to a higher (lower) value. To incorporate such impact of large size market orders,
we choose to use a jump diffusion process, which is a combination of a diffusion
process and a compound poisson process, to simulate the path of a stock's mid
price.
Based on the jump diffusion process that the underlying asset should follow, we
propose the Hamilton-Jacobi-Bellman equation by the knowledge of stochastic
control and dynamic programming principle. The HJB equation is an partial
integro-differential equation that the optimal bid and ask quotes δ
a and δ
b should
satisfy. Finally, we find the approximate expression of δ
a and δ
b by using taylor
expansion and polynomial approximation of the utility function. The expression
for δ
a and δ
b is the market making strategy under a jump diffusion process in a
finite time horizon, and we call it 'jump' strategy.
Lastly, we evaluate the performance of our 'jump' strategy by implementing it
into simulated path of stock's price and real tick data of a stock Exxon Mobil
Corporation. In addition, we also implement the traditional 'continuous' strategy, which is based on a diffusion process, into both simulated data and real
data. Comparing the sharp ratio value of two strategies, the performance of our
'jump' strategy is generally better than that of the 'continuous' strategy.
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