Collateralization is a critical component of the plumbing of the financial system. The use of collateral in financial markets has increased sharply over the past decade, yet analytical and empirical research on collateralization is relatively sparse. The effect of collateralization on valuation and risk is an understudied area.

The counterparty exposures are significantly affected by the existence of collateral agreement (unilateral or bilateral), the type of derivatives and collateral assets, and the definition of collateral agreements (margin call frequency, threshold, etc.). This collateral methodology provides a testing platform to check the impact of these factors and provides guidance for the Bank to make decisions regarding trading activities and collateral agreements.

Due to the complexity of collateralization, literature seems to turn away from direct and detailed modeling. For example, Johannes and Sundaresan [2007], and Fuijii and Takahahsi [2012] model collateralization via a cost-of-collateral instantaneous rate. Piterbarg [2010] regards collateral as a regular asset and uses the replication approach to price collateralized derivatives.

Schmalz et al (2016) find that an increase in collateral value leads to a higher probability of becoming an entrepreneur. Lian and Ma (2019) present evidence that the borrowing of US non-financial firms correlates with their transaction volumes, as measured by earnings. Different forms of constraints also have different implications for credit allocation and efficiency, responses to monetary policy, economic recovery and the rise of intangible capital.

Ioannidou et al (2019) show that a 40% drop in collateral values would lead almost a quarter of loans to become unprofitable, a reduction of average demand by 16% and a drop in banks’ expected profits of 25%. Benmelech et al. (2020) find that a firm limits its flexibility to sell or redeploy assets to craft a better business operation by pledging collateral and a significant decline in the fraction of secured debt among US firms over the twentieth century.

Ghamami et al. (2022), which analyze the interaction between the counterparty and price channel of spillovers. Demarzo (2019) addresses that collateral can be a cost-e_cient commitment device, and Donaldson et al. (2020) argue that secured debt prevents debt dilution.

Contrary to previous studies, we present a model that characterizes a collateral process directly based on the fundamental principle and legal structure of CSA. The model is devised that allows for collateralization adhering to bankruptcy laws. As such, it can back out price changes due to counterparty risk and collateral posting. Our model is very useful for valuing off-the-run or outstanding derivatives.

This article makes theoretical and empirical contributions to the study of collateralization by addressing several essential questions. First, how does collateralization affect swap rate?

Interest rate swaps collectively account for two-thirds of all outstanding derivatives. An ISDA mid-market swap rate is based on a mid-day polling. Dealers use this market rate as a reference and make some adjustments to quote an actual swap rate. The adjustment or swap premium is determined by many factors, such as credit risk, liquidity risk, funding cost, operational cost and expected profit, etc.

Unlike generic mid-market swap rates, swap premia are determined in a competitive market according to the basic principles of supply and demand. A swap client first contacts a number of swap dealers for a quotation and then chooses the most competitive one. If a premium is too low, the dealer may lose money. If a premium is too high, the dealer may lose the competitive advantage.

Portfolio valuation, when aggregated with collateral valuation, determines the collateralized exposure. The portfolio value at time t equals its liquidation value plus the cash flow adjustments. Although the MTM (market-to-market) value at t is observable, the liquidation value observable at the end of liquidation period reflects the true replacement cost. These two values may become very different when the market is very volatile, or the liquidity becomes very low (e.g. during the 2008 financial crisis).

Empirically, we obtain a unique proprietary dataset from an investment bank. We use these data and a statistical measurement