A Derivatives Pricing Model with Non-Cash Collateralization

Abstract

This article proposes a derivatives pricing model with both cash and a non-cash asset posted as collateral for a derivatives contract. We assume that the participant sources funds from the repo market for the posted non-cash collateral. Our pricing formula is based on the investment of the received collaterals. For the pricing formula, we discount the future derivatives value using a combination of the collateral and repo rates under a risk-neutral measure. Thus, our pricing model constructs a multi-curve framework. We calibrate our pricing model for JPY interest rate derivatives and then show that our model with non-cash collateralization is closer to the real price than the existing pricing formulae (i.e., the cash collateralization and simple short rate models).

TOPICS: Derivatives, interest-rate and currency swaps, quantitative methods, statistical methods, risk management, credit risk management

Key Findings

• ▪ A derivatives pricing model when cash and a non-cash asset are posted as collateral is proposed. The non-cash collateral receiver exchanges the posted collateral for cash in the repo market.

• ▪ Under this framework, the discount rate in the resulting pricing formula is given as the weighted average of the collateral and repo rates weighted with the amount of the cash collateral.

• ▪ The accuracy of the proposed pricing formula is superior to the pricing formula with the OIS discount that has been common after the financial crisis in 2008.