Question

Absence of price manipulation strategies This exercise finds a lower bound on the decay parameter βt​ of a generalized OW model based on a liquidity profile vt​ to rule out price manipulation trategies. Assume the intraday volume profile v follows the deterministic vt​=e4⋅(t−0.7)2. Local square root model under the calendar clock I The impact model considered is dIt​=−βIt​dt+vt​​λ​dQt​ 1. Establish the lower bound on β that guarantees no price manipulation. 2. For β=0.01, find a pair of trades that lead to a price manipulation paradox. Local log model under the volume clock II The impact model considered is dIt​=−βvt​It​dt+vt​λ​dQt​ 1. Establish a lower bound on β that guarantees no price manipulation. 2. For β=0.01, find a pair of trades that lead to a price manipulation paradox

Answer 1

In this exercise, we need to find the lower bound on the decay parameter βt in order to rule out price manipulation strategies. We also need to establish a lower bound on β that guarantees no price manipulation.

Step-by-step explanation:

In the first part of the exercise, we need to find the lower bound on the decay parameter βt in order to rule out price manipulation strategies. The given liquidity profile vt follows the formula vt=e4(t−0.7)2. To establish the lower bound on β, we need to ensure that the impact model dIt=−βItdt+vtλdQt does not allow for price manipulation. The lower bound on β can be found by considering the conditions that prevent price manipulation.

In the second part of the exercise, we are given the impact model dIt=−βvtItdt+vtλdQt. We need to establish a lower bound on β that guarantees no price manipulation. Similar to the previous part, we need to consider the conditions that prevent price manipulation and find the appropriate lower bound on β.