Minimising transaction costs is important for best execution. While existing research minimises the cost of a single trade, our results optimise the combined execution cost of two sequential orders.
Minimising transaction costs is important for best execution. While existing research minimises the cost of a single trade, our results optimise the combined execution cost of two sequential orders.
March 2023
We obtain the optimal execution strategy for two sequential trades in the presence of a transient price impact. We first present a novel and general solution method for the case of a single trade (a metaorder) that is executed as a sequence of sub-trades (child orders). We then analyze the case of two sequential metaorders, including the case where the size and direction of the second metaorder are uncertain at the time the first metaorder is initiated. We obtain the optimal execution strategy under two different cost functions. First, we minimize the total cost when each metaorder is benchmarked to the price at its initiation, the total separate costs approach widely used by practitioners. Although simple, we show that optimizing total separate costs can lead to a significant understatement of the real costs of trading whilst also adversely impacting order scheduling. We overcome these issues by introducing a new cost function that splits the second metaorder into two parts, one that is predictable when the first metaorder is initiated and a residual that is not. The predictable and residual parts of the second metaorder are benchmarked using the initiation prices of the first and second metaorders, respectively. We prove existence of an optimal execution trajectory for linear instantaneous price impact and positive definite decay, and derive the explicit form of the minimizer in the special case of exponentially decaying impact, however uniqueness in general remains unproven. Various numerical examples are included for illustration.
You are now exiting our website
Please be aware that you are now exiting the Man Institute | Man Group website. Links to our social media pages are provided only as a reference and courtesy to our users. Man Institute | Man Group has no control over such pages, does not recommend or endorse any opinions or non-Man Institute | Man Group related information or content of such sites and makes no warranties as to their content. Man Institute | Man Group assumes no liability for non Man Institute | Man Group related information contained in social media pages. Please note that the social media sites may have different terms of use, privacy and/or security policy from Man Institute | Man Group.