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A cash flow with present value (PV) $2m at 265 days is to be mapped to interest rates with maturities 6 months and 12 months.

A cash flow with present value (PV) $2m at 265 days is to be mapped to interest rates with maturities 6 months and 12 months. These interest rates have volatilities 75bps and 90bps respectively, and correlation 0.75. The vertex at 265 days has volatility 85bps The mapping must preserve both PV and volatility. How much, in PV terms, is mapped to each vertex?

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