Choosing Discount and Forward Curves for Derivative Valuation

Summary

The document distinguishes zero rates, used to derive discount factors for valuing cash flows today, from forward rates, which are implied by zero rates and no-arbitrage relationships to describe rates over future periods. It frames curve selection as dependent on the cash flows and product being valued. For example, an interest rate swap with future cash flows may require a forward curve to project those cash flows, while discounting uses the appropriate discount factors.

The discussion offers only a brief conceptual answer to questions about curve assignment and credit risk. It does not give product-by-product rules, explain modern multi-curve frameworks, or specify how short versus long maturities affect the choice. Its practical takeaway is to identify the cash flows being projected or discounted and apply the curve appropriate to that role; product conventions and risk-purpose details require further context.

Key ideas

• Zero rates determine discount factors for valuing cash flows at present value.
• Forward rates are implied from zero rates under no-arbitrage assumptions and describe future-period rates.
• Curve choice depends on the product and whether cash flows need projection or discounting.
• The document does not provide specific curve-selection rules for credit risk or maturity buckets.

Tags

# Discount Curve Vs Forward Curve


# Discount Curve Vs Forward Curve












This could be a trivial question, but would I like to clear the concepts.

Our firm started sourcing the Murex Trades which has all the variety of Derivative products. I noticed that the Curve Assignment service has two types being Used:

- Discount Curve

- Forward Curve

I noticed that both curves are mapped to most of the products. Can you please confirm the following:

- In general whats the criteria for selection of the type of curve?

- Does it generally differs for Short Term maturing Products and Long Term maturing products?

- Do we need to consider both curves for Credit Risk purpose?

Thanks in advance

## Answer by Ryan J. Shrott (score -2)

https://quant.stackexchange.com/a/36184

You should first understand the difference between a forward rate and a zero rate. The zero rates are what you would normally think of: the discount factor to get the value of a cash flow today. The forward curves are implied discount factors calculated using zero rates which give discount factors in the future under no arbitrage assumptions.

The computation of forward rates are trivial. Wiki reference is the best if you forget the calculation: https://en.wikipedia.org/wiki/Forward_rate

- It's a function of what you want to discount. For example, if you were valuing cash flows in the future, (i.e. interest rate swap), you would use a forward curve.

- Depends on the product

- Depends on the product

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