Reducing a Swaption Vega Matrix While Preserving Total Risk

Summary

The document poses a risk aggregation problem for an interest rate swaption matrix organized by expiry and tenor. It asks how to compress a larger grid into a smaller set of buckets while keeping the sum of instrument vegas unchanged. The example describes a 24-expiry by 10-tenor matrix reduced to a 7-by-8 matrix, with total vega as the stated constraint.

No solution, aggregation rule, or validation evidence is provided; the text is a request for methodological guidance. Preserving the arithmetic sum alone may not preserve the portfolio’s actual exposure profile, since offsetting signs, bucket sensitivities, and the mapping from original instruments to new buckets could matter. The document therefore identifies a useful problem in risk representation but does not teach a specific method or establish that any proposed reduction is adequate.

Key ideas

• The problem is to compress a swaption expiry-tenor grid into fewer risk buckets.
• The stated constraint is equality between the total vega in the original and reduced matrices.
• The document gives no method for assigning instruments to buckets or validating the approximation.
• A preserved aggregate may not capture the full distribution of exposure across expiries and tenors.

Tags

# Swaption risk bucketing


# Swaption risk bucketing












In the IR swaption market, we have 24Expire10Tenor instruments(like a 2410 Matrix). Now I have the Vega number for each instrument, and I want to reduce the matrix size with the same total vega risk.

Matrix A(2410) to Matrix B(78), constrain by sum(A)=sum(B) Any hint for this problem? What method should I think about it? Thanks a lot!

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