Pricing Floating-Rate Notes from Discount Margin
Summary
The discussion explains how a known discount margin (DM) can be used to estimate the price of a floating-rate note. For a simple floater, DM can be understood as the reference index plus the coupon spread and an additional yield component reflecting any price difference from par over the note’s remaining life. This relationship can be worked backward to infer price from DM; a cash-flow discounting function is also mentioned as a practical route.
The example compares a five-year note paying EURIBOR plus 50 basis points at a price of 99.50, and illustrates an approximate annual spread contribution from the discount to par. The answer notes that more complex floaters may require assumptions about index rates and prepayments, while calculating option-adjusted spread requires a model. The simple relationship is therefore most suitable for straightforward floaters and is not a general substitute for a full cash-flow or option model.
Key ideas
- For a simple floater, discount margin reflects the coupon margin plus the effect of price deviation from par over the note’s life.
- A known discount margin can be used in reverse to estimate a floating-rate note’s price.
- Cash-flow discounting can provide a practical way to calculate price from discount margin.
- Option-adjusted spread requires a model, and more complex floaters may need additional assumptions.
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Full text
# For a Floating Rate note, is there a way to convert the Discount Margin into OAS or Price? # For a Floating Rate note, is there a way to convert the Discount Margin into OAS or Price? Sorry if this is a very basic or flawed question but I am struggling. I have a known Discount Margin and I am ultimately looking to compute a price from this value as I do not have one. Alternative if its possible to convert to OAS that would work too as I can then use that in my Price Calculator. All the information I have if the Maturity Date and Spread to the EURIBOR and have assumed a Quarterly reset and payment frequency. Any help and suggestion would be greatly appreciated. Thanks in advanced. ## Answer by Dom (score 1) https://quant.stackexchange.com/a/66606 If you use Python, check out this example notebook on FinancePy https://github.com/domokane/FinancePy/blob/master/notebooks/products/bonds/FINBONDFRN_CitigroupExample.ipynb The function you need is full_price_from_dm ## Answer by Edward Watson (score 0) https://quant.stackexchange.com/a/46969 you need to use a cashflow generator that can discount the cash flows like bloomberg. Convention for CMO floaters is to hold the index constant with a reasonable prepayment assumption (PSA/CPR) and use the market DM to get a price. Calculating OAS requires a model. ## Answer by dm63 (score 0) https://quant.stackexchange.com/a/46970 For a simple floater, the discount margin over the reference index equals the coupon margin plus the price discount to par (if any) spread over the life of the note. Thus, it is like yield to maturity for floaters. For example 5yr maturity Coupon = euribor + 50 Price = 99.50 Then the discount to par is 0.50% which is worth about 10bp per annum on a 5yr. Therefore the yield on the bond is equivalent to euribor + 60 and the discount margin is 60. You can also run this backwards to get price from discount margin.
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