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I am trying to model the price impact in stress for a period of several days.

Specifically, I am looking for a function/model that predicts the price movement

  1. Given a set of ex-ante factors (e.g: liquidity, implied volatility, etc.) and
  2. As a function of the volume size (proxy for the intensity of the stress)

Price impact models typically assess the impact of a) individual orders (including meta-orders), b) under normal market conditions and c) over short horizons (minutes). Under a) to c), empirical analyses find that the price impact is typically a concave function of order size, progressively smaller market impact as volume grows.

In contrast to traditional models, I would like to model the impact of a') market-wide aggregate dynamics (including correlated orders / herding behaviors), b') calibrated under stress (with potentially reduced liquidity and downward price spirals) and c') over an horizon of several days (which reinforce possible negative feedback loops).

Could someone give me some ideas regarding:

  • Which explanatory factors could be used: market depth, implied vol, ….?.
  • Which models or impact functions: concave, convex, two-step (e.g: concave and convex), others?

PS: I am aware that this question is at the boundary between market microstructure and risk management. It would be helpful to hear your views regarding the benefits of extending price impact models to (short) horizons that may be covered by risk management models (e.g: stochastic processes or historical analysis).

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    $\begingroup$ I discuss market depth & execution strategies here. It's not exactly what you're after but might give some food for thought... $\endgroup$ – Jan Stuller Jan 29 at 13:14
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I will attempt to elaborate on this from risk management perspective.

  1. scenario analysis approach: An example of this is stress testing that Fed mandates for investment banks. Fed gives stress variables to various fundamental macro variables. For example, a certain market stress scenario will be rates down 100bps, volatility up 30%, curve flatter by 30bps, corporate spreads wider 200bps, High yields wider by 1000bps etc etc. Once you have these macro variable shocks, you just use these inside your stochastic or fundamental models and recompute price of portfolio you own. Based on how much your portfolio can lose, it becomes measure of your loss in that scenario.

  2. Simulation approach: Another approach can be building models where you play out worse 10 day period etc. if your distributions were normal, this would mean that sigma_10day = sqrt(10) * sigma_1d. However, since returns have fat tails, you would have to look at empirical distribution and simulate your portfolio through worse 10 days.

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