Ebook Discounting Revisited. Valuations under Funding Costs, Counterparty Risk and Collateralization.
Looking at the valuation of a swap when funding costs and counterparty risk are neglected (i.e., when there is a unique risk free discounting curve), it is natural to ask “What is the discounting curve of a swap in the presence of funding costs, counterparty risk and/or collateralization”.
The answer depends on who you are and how we value. Factoring in funding costs the answer to that question is “There is no such thing as a unique discounting curve (for swaps).”
Contents
1 Introduction
1.1 Two Different Valuations
2 Discounting Cash Flows: The Third Party (Mark-to-Market) Liquidation View
2.1 Discount Factors for Outgoing and Incoming Cash Flows
- 2.1.1 Valuation of a Fixed Coupon Bond
2.2 Counterparty Risk
- 2.2.1 Example
2.3 Netting
2.4 Valuation of Stochastic Cash Flows
2.5 Credit Linking
- 2.5.1 Examples
2.6 Collateralization
- 2.6.1 Interpretation
2.6.2 Example
2.6.3 Full Bilateral Collateralization
3 Discounting Cash Flows: The Hedging View
3.1 Moving Cash Flow through Time
- 3.1.1 Moving Positive Cash to the Future
3.1.2 Moving Negative Cash to the Future
3.1.3 Hedging Negative Future Cash Flow
3.1.4 Hedging Positive Future Cash Flow
3.2 Construction of Forward Bonds
- 3.2.1 Forward Bond 1: Hedging Future Incoming Cash with Outgoing Cash
3.2.2 Forward Bond 2: Hedging Future Outgoing Cash with Incoming Cash
3.2.3 Forward Bond 1’: Hedging Future Credit Linked Incoming Cash with Credit Linked Outgoing Cash
3.2.4 Price of Counterparty Risk Protection
3.2.5 Example: Expressing the Forward Bond in Terms of Rates
3.2.6 Interpretation: Funding Cost as Hedging Costs in Cash Flow Management
3.3 Valuation with Hedging Costs in Cash flow Management (Funding)
- 3.3.1 Interest for Borrowing and Lending
3.3.2 From Static to Dynamic Hedging .
3.3.3 Valuation of a Single Product including Cash Flow Costs
3.3.4 Valuation within a Portfolio Context - Valuing Funding Benefits
3.4 Valuation with Counterparty Risk and Funding Cost
- 3.4.1 Counterparty Risk in the Absence of Netting
3.4.2 Counterparty Risk in the Presence of Netting
3.4.3 Interpretation
4 The Relation of the Different Valuations including Counterparty Risk
5 One Product - Two Values
5.1 ValuationofaBond
- 5.1.1 Valuation of a Bond at Mark-To-Market
5.1.2 Valuation of a Bond at Funding
5.2 Convergence of the two Concepts
6 Credit Valuation Adjustments
7 Modeling and Implementation
8 Other Work
9 Conclusion
References
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