If a trader needs to unwind a large position, he or she is exposed to:
- the potential loss from price movements, and
- trading liquidity risk
The trader may wish to minimize the Value-at-Risk (VaR) after considering the trading costs (or cost of liquidation). What is the optimal trading strategy then to achieve the trader’s objective?
Part 1 (Concept and Motivation)
The video explains the concept and define the problem set. At the end, I will use a simple case which will be the input to Part 2.
Part 2 (Building the model)
Using the parameters from the Case in Part 1, in this video, I walk through the model building in Excel. I will model the VaR of the position outstanding at the end of each day and the cost of liquidating the position every day. The objective is to minimize the VaR + cost of liquidation over the trading period.
In this model, I assume liquidation in a normal market. If there is a stressed market scenario, the cost of liquidation can be modeled as (mean bid-offer spread + Z * standard deviation of bid-offer spread), where Z is the inverse of a cumulative distribution function (e.g. normal distribution).