JPSem

This makes sense, but it isn’t a function of volatility to me.  Saying that the value increases because of an increase in volatility means you should be saying: “investors are willing to pay more for a bond that gives them the right to sell it at a price that rises or falls a lot.”
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Yeah you are getting it right! Investors are willing to pay more for more volatility.
I even agree with what S2000Magician has explained.. he has given a very gud example too.
The logic is all this “increased volatility means increased possibility of making increasing gains”.. And being a put option, in case the price rises, he has the RIGHT not to exercise the option(I am sure you know this).. Thus forget the fact of prices going up for a put option holder.. If he expects volatility of the prices to be very high, he expects the price to fall steeply and thus make gud profit..
Correct me if i m missing something