Liability-side Pricing of Swaps and Coherent CVA and FVA by Regression/Simulation

TL;DR

This paper introduces a regression/simulation approach for liability-side swap pricing, incorporating coherent CVA and FVA, and demonstrates how dynamic hedging and discount rate switching improve valuation accuracy.

Contribution

It presents a novel method combining regression and simulation to accurately compute swap valuation adjustments, including CVA and FVA, with dynamic hedging and discount rate switching.

Findings

Dynamic hedging with CCP swaps can fully replicate uncollateralized swaps.

The proposed method reduces errors in CVA calculation compared to traditional discounting.

Counterparty risk significantly impacts hedge ratios, bid/ask spreads, and valuation adjustments.

Abstract

An uncollateralized swap hedged back-to-back by a CCP swap is used to introduce FVA. The open IR01 of FVA, however, is a sure sign of risk not being fully hedged, a theoretical no-arbitrage pricing concern, and a bait to lure market risk capital, a practical business concern. By dynamically trading the CCP swap, with the liability-side counterparty provides counterparty exposure hedge and swap funding, we find that the uncollateralized swap can be fully replicated, leaving out no IR01 leakage. The fair value of the swap is obtained by applying to swap's net cash flows a discount rate switching to counterparty's bond curve if the swap is a local asset or one's own curve if a liability, and the total valuation adjustment is the present value of cost of funding the risk-free price discounted at the same switching rate. FVA is redefined as a liquidity or funding basis component of total valuation adjustment, coherent with CVA, the default risk component. A Longstaff-Schwartz style least-square regression and simulation is introduced to compute the recursive fair value and adjustments. A separately developed finite difference scheme is used to test and find regression necessary to decouple the discount rate switch. Preliminary results show the impact of counterparty risk to swap hedge ratios, swap bid/ask spreads, and valuation adjustments, and considerable errors of calculating CVA by discounting cash flow or potential future exposure.