Hi Shruti,
The cdsbootstrap function in MATLAB is part of the Financial Instruments Toolbox and is used for bootstrapping credit default swap (CDS) spreads to extract default probabilities and hazard rates. The methodology underlying this function involves several steps and assumptions, primarily focusing on constructing a term structure of default probabilities that is consistent with the observed market prices of CDS contracts.
Here is a high-level overview of the methodology typically involved in bootstrapping default probabilities from CDS spreads:
Input Data
- ZeroData: Information about the risk-free interest rate term structure. This can include zero rates, discount factors, or yield curve data used for discounting cash flows.
- MarketData: Market data for CDS contracts, which usually includes CDS spreads for various maturities.
- Settle: The settlement date for the CDS contracts, which is the reference date for the bootstrap process.
Bootstrapping Process
The bootstrapping process involves iteratively solving for the default probabilities that make the theoretical price of a CDS contract equal to its market price. This process typically involves the following steps:
- Step 1: Start with the shortest maturity CDS and assume an initial default probability curve (often starting with a flat curve or using market heuristics).
- Step 2: Calculate the theoretical price of the CDS using the assumed default probability curve and the risk-free rate curve to discount cash flows. The cash flows considered in a CDS include premium (spread) payments and the contingent payment in case of default.
- Step 3: Adjust the default probability curve so that the theoretical price of the CDS matches its market price. This involves solving for the hazard rate (or default intensity) that aligns the theoretical and market prices.
- Step 4: Move to the next maturity CDS and repeat the process, using the previously solved default probabilities as the starting point. This step involves ensuring that the default probability curve is consistent across maturities.
- Step 5: Continue the process until default probabilities for all maturities have been solved.
Output
- ProbData: The bootstrapped default probabilities, typically expressed as a term structure showing the probability of default by different future dates.
- HazData: The hazard rates derived from the bootstrapping process. Hazard rates are related to default probabilities and provide an instantaneous measure of default risk.
Methodological Assumptions
- Piecewise Constant Hazard Rates: The methodology often assumes that hazard rates are piecewise constant between CDS maturities.
- Recovery Rates: Assumptions about recovery rates in case of default are crucial, as they affect the contingent payment calculations.
- Market Frictions: The methodology typically abstracts away from market frictions, taxes, and counterparty risk.
Refer to this documentation for more details: https://in.mathworks.com/help/finance/cdsbootstrap.html
