How Model Prices Can Conceal Liquidity Risk
Summary
The discussion explains why a portfolio valued through a theoretical replicating model may carry more risk than its model-based VaR suggests. Convertible bonds illustrate the issue: their theoretical values depend on factors such as volatility, interest rates, and credit spreads, while actual market prices can diverge substantially. If a position must be liquidated during such a divergence, the modeled hedge may not reflect the price available in the market.
A further risk arises when many market participants react to the same signal and try to exit together, reducing available liquidity and increasing liquidation losses. The answers distinguish ordinary market-impact estimates, such as square-root models, from models fitted to extreme events; estimating the time required to unwind may also matter. The discussion offers conceptual guidance rather than a calibrated method or empirical evidence, and notes that stress testing can help address risks omitted by a replicating-portfolio VaR.
Key ideas
- A replicating portfolio can miss losses when a convertible bond's market price diverges from its theoretical value.
- Market risk models may understate liquidation losses when they assume trades can be executed near modeled prices.
- Crowded exits can drain liquidity and amplify losses across otherwise similar positions.
- Ordinary market-impact models and models fitted to extreme events address different liquidity conditions.
- Stress testing can help expose risks that a replicating-portfolio VaR overlooks.
Tags
Full text
# How are we underestimating liquidity risk? # How are we underestimating liquidity risk? Malz explains that marking to model can underestimate liquidity risk. From his example, I don't see it. I can see us underestimating market risk because we are using an incorrect price. Why does a divergence between the market and model prices cause liquidity risk ? > Another example is convertible bond trading. Convertible bonds can be mapped to a set of risk factors including implied volatilities, interest rates, and credit spreads. Such mappings are based on the theoretical price of a convertible bond, which is arrived at using its replicating portfolio. However, theoretical and market prices of converts can diverge dramatically. These divergences are liquidity risk events that are hard to capture with market data, so VaR based on the replicating portfolio alone can drastically understate risk. Stress testing can mitigate the problem. ## Answer by Sergey Bushmanov (score 2, accepted) https://quant.stackexchange.com/a/21227 In order for the risks of a presumably "correct" model to realize in practice, there should be enough liquidity in the market. This is what he is referring to when saying > [...] liquidity risk events that are hard to capture with market data, so VaR based on the replicating portfolio alone can drastically understate risk The problem with many models is the fact that when your model raises red flag, there are thousands of similar models at others' traders, that raise red flags too. Too many people rushing to the exit at the same time, no liquidity at all. This is called Liquidity risk (or lack thereof): [in]ability to quickly liquidate your position without significant loss (or at preconceived price, if you wish). I believe Taleb in his "Fooled by Randomness" discussed this issue (and issues with VaR) in detail. ## Answer by lehalle (score 2) https://quant.stackexchange.com/a/21263 I agree with @bushmanov about "running for exit", but I would like to underline an important point. In the question you stated "marking to model can underestimate liquidity risk." It is not true since you will need a model to estimate liquidity risk. You have two kinds of models that for: - usual market impact models. If there is not that much people running for exit, square root based models will be good enough. You may nevertheless need another model to compute the time needed to get rid pf your position, like stopping time computations. - models fitted on extreme events.
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