Rates and curves

Part 1 defined a discount factor for one future date from a rate quote, and Part 2 applied one discount factor to each promised bond payment. This part collects the discount factors of many dates into one deterministic discount curve. The credit-curve chapter of Part 7 uses that curve as the risk-free discount input of a CDS.

This part has one chapter. It reads a deterministic discount curve that is input at a set of dates, interpolates log-linearly between those dates, and calculates the forward discount factor between two future dates as the ratio of their discount factors from valuation time. The curve is an input: the chapter does not calibrate it to market prices, and it does not extrapolate beyond the last input date.

Part 3 of 71 chapter1 numbered equations1 knowledge check

1. Discount curve and forward discounting

   Move from one discount factor to a dated deterministic curve and derive future-to-future discount factors.

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The argument

1. A discount curve holds one discount factor for each input date
2. Log-linear interpolation gives the dates between the inputs
3. The ratio of two discount factors discounts from one future date to another

After this part you can

• Interpret a dated set of positive valuation-time discount factors as a deterministic curve, including its interpolation and no-extrapolation conventions.
• Calculate the deterministic discount factor between two future model times from their valuation-time discount factors.

Builds on

• Foundations

Leads to

• CDS