Ebook A Beginner’s Guide to Credit Derivatives
This document will attempt to describe how simple credit derivatives can be formally represented, shown to be replicable and ultimately priced, using reasonable assumptions. It is a beginner’s guide on more than one count: its subject matter is limited to the most simple types of claims (those involved in credit default swaps, plus a few more) and its treatment so detailed that most beginners should be able to follow it.
Basic definitions of general option pricing are also included to establish a common and consistent terminology, and to avoid any possible misunderstanding. It is also a beginner’s guide in the sense that I am myself a complete beginner on the subject of credit. I have no trading experience of credit default swaps, and my modeling background is limited to that of the default-free world.
When I became acquainted with the concept of credit default swap (CDS’s), and was told about their rising importance and liquidity, I was struck by the obvious parallel that could be drawn between interest rate swaps (IRS’s) with their building blocks (the default-free zeros), and CDS’s with their own fundamental components (the risky zeros). In the early 1980’s, the emergence of IRS’s and the realization that these could be replicated with almost static trading strategies in terms of default-free zeros, rendered the whole exercise of bootstrapping meaningful.
The ultimate simplicity of default-free zeros, added to the fact that their prices could now be inferred from the market place, made them the obvious choice as basic tradable instruments in the modeling of many interest rate derivatives. Having assumed default-free zeros to be tradable, the whole question of contingent claim pricing was reduced to the mathematical problem of establishing the existence of a replicating strategy: a dynamic trading strategy involving those default-free zeros with an associated wealth process having a terminal value at maturity, matching the payoff of the given claim.
Contents
1 Introduction
2 Trading Strategies and Replication
- 2.1 Contingent Claims
2.2 Stochastic Processes
2.3 Tradable Instruments and Trading Strategies
2.4 The Wealth Process
2.5 Replication and Non-Arbitrage Pricing
3 Credit Contingent Claims
- 3.1 Collapsing Numeraire
3.2 Delayed Risky Zero
3.3 Credit Default Swap
3.4 Risky Floating Payment and Related Claim
3.5 Foreign Credit Default Swap
3.6 Equity Option with Possible Bankruptcy
3.7 Risky Swaption and Delayed Risky Swaption
3.8 OTC Transaction with Possible Default
A Appendix
- A.1 SDE for Cash-Tradable Asset and one Numeraire
A.2 SDE for Futures-Tradable Asset and one Numeraire
A.3 SDE for Funded Asset and one Numeraire
A.4 SDE for Funded Asset and one Collapsing Numeraire
A.5 SDE for Collapsing Asset and Numeraire
A.6 Change of Measure and New SDE for Risky Swaption
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