UPDATE 1-Hiscox, Beazley post 9-month premium jump

* Hiscox gross written premiums up 32 percent

* Beazley premiums up 45 percent

* Hiscox shares up 3 percent, Beazley up 1.5 percent

(Adds detail)

LONDON, Nov 9 (Reuters) - London-listed insurers Hiscox (HSX.L) and Beazley (BEZG.L) both posted strong rises in premium income for the first nine months of the year and said on Monday they had seen stable or increased rates over the period.

Bermuda-based Hiscox said premium income in the first nine months of the year rose 31.7 percent to 1.2 billion pounds ($2 billion), as its London market business, helped by a benign third quarter, was complemented by strong growth in its international arm and Europe returned to profit. On constant exchange rates, that year-on-year rise was 10.5 percent.

The news boosted its shares, trading up 3.1 percent by 0804 GMT at 338p, against a 1.8 percent rise in the European index of insurance stocks .SXIP. Beazley was also trading higher, changing hands at 109.3p, up 1.5 percent.

"Rates are stable and still very healthy in most areas, particularly reinsurance which accounts for over a third of our business," Chairman Robert Hiscox said in a statement.

Hiscox said it was taking advantage of a hardening of reinsurance rates in Bermuda, where it saw 53.4 percent growth in sterling terms, while growth in its Guernsey business was being driven by kidnap and ransom lines and piracy insurance.