A Roth conversion is a distribution and taxable rollover. IRA custodians perform the distribution after market close, so the value of the converted stock is the value that it has at the next market close following receipt of your instruction to distribute or convert. If your instruction to distribute or convert is received by the IRA custodian while the market is open, the distributed asset will be valued later that same day the close of the market. If your instruction to convert is received after market close on a particular day, the distributed asset will be valued at the close of the market on the next day that the market is open. The value at a close of the market prior to receiving your conversion instruction is never used. Every Roth conversion I've ever done has been accompanied by a notice indicting that the distribution will be valued at the next market close.
What you might be thinking of is the case where there is a delay in making the conversion contribution, such as what happens if you receive an in-kind distribution of stock from the traditional IRA , then, say, a week later make a Roth conversion contribution of the same shares to a Roth IRA. Even though the receiving Roth IRA custodian will report on Form 5498 a conversion contribution of the value of the shares on the date of the conversion contribution, this still constitutes a conversion of the value on the distribution date. If this happens, it might be prudent to provide an explanation statement to the IRS that the value of the conversion contribution differs from the amount converted due to the change in the value of the stock between the distribution and the contribution. If the conversion is done in-house, though, the conversion contribution will have that same value as the distribution and this won't be an issue. In either case, the amount converted is the amount shown in box 1 of the Form 1099-R.
