AMENDMENT TO ARCH CAPITAL GROUP LTD. 2007 EMPLOYEE SHARE PURCHASE PLAN

Exhibit 10.8.2

AMENDMENT TO
ARCH CAPITAL GROUP LTD.
2007 EMPLOYEE SHARE PURCHASE PLAN

The Arch Capital Group Ltd. 2007 Employee Share Purchase Plan is amended as set forth below, effective November 7, 2007.

1.             The first sentence of Section 7(c) of the Plan is amended to read as follows:

“Any balance remaining in an employee’s payroll deduction account after shares have been purchased in an Offering pursuant to Section 8(b) below will be refunded to the Participating Employee, except that, unless otherwise determined by the Committee, any such remaining balance in an amount representing a fractional share shall be carried forward and applied, subject to the Participating Employee’s withdrawal right, toward the purchase of additional stock by the Participating Employee in the subsequent Offering.”