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Interest rates on enbedded bonds

Hi guys,
i like to seek some confirmation if my understanding is correct.

When there is a rise in volatility,
1) it increase value of call option and decrease market value of callable bond
2) increase value of put option and decrease market value of put bond

As for the rise in interest rates, it decrease the value of putable bonds and increase the value of callable bonds.

Am i right?

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