Building a Discount Curve from Spot Rates to Price Bond Cash Flows

Summary

The document presents a bond valuation question: how to discount a schedule of coupon and principal payments using quoted spot rates, while also applying a credit spread. The author compares a spreadsheet calculation with a valuation engine and asks whether the mismatch between the curve’s quoted maturities and the cash-flow dates explains the difference. The cash flows occur at fractional-year dates, while the listed curve points are annual maturities.

The material identifies the key modeling issue but does not provide a worked solution or establish the correct price. To construct a valuation, a practitioner needs discount factors aligned to each payment date, which generally requires a defined interpolation convention and clarity about rate compounding, day-count basis, and spread application. The document therefore serves as a setup for investigating curve construction rather than evidence that a particular interpolation or valuation method is correct. No answer in the supplied text reconciles the engine’s result with the spreadsheet.

Key ideas

• Bond cash flows should be discounted using factors matched to their payment dates.
• Cash-flow dates between quoted spot maturities require an interpolation or curve-construction convention.
• A credit spread affects discounting, but its application depends on the valuation setup.
• The document raises a pricing discrepancy without supplying enough information to resolve it.

Tags

# Discount curve from spot rates for bond pricing


# Discount curve from spot rates for bond pricing












I have a bond with the following cash flow and maturity:

```
Cash flow vector    Maturity
4                   0.479452055
4                   1.479452055
4                   2.479452055
4                   3.479452055
104                 4.479452055
```

I want to derive the price by discounting using the spot curve (see Excel-File for exact values) per 2015-12-31 and a credit spread of 0,054430033:

```
 Spot Curve   Maturity
 -0.8%         1
 -0.8%         2
 -0.8%         3
 -0.7%         4
 -0.5%         5
```

I tried this in the Excel-Spreadsheet (over here), however the prices I calculate differ from the price of my bond valuation engine where 98.22 is provided (in two programmes independently). I guess the discount factors I use are wrong. Yet I do not know how to construct the proper discount curve with these inputs. Can you please point me to the right direction?

Update: I have been thinking about my issue and spotted a maturity mismatch since the spot curve is provided for maturity 1 to 10 whilst my first cash flow is at 0.479 - probably this is a problem as well?

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This summary was written by Stratmill's research agent from the original; it is not a copy of the source.