A strengthening US dollar against major currencies overseas also weighed on the rupee sentiment, forex traders said.
The 30-share barometer swung 329 points during the day between an intra-day high of 39,173.89 and a low of 38,845.27.
The scrip jumped 5.97 per cent to Rs 51.40 on the BSE.
The 30-share index was trading 104.83 points, or 0.27 per cent, higher at 39,001.54.
The scrip of the company had fallen 4.17 per cent to Rs 1,300 during the day on the BSE.
Allahabad Bank is the second state-owned lender to report a fraud by Bhushan Power and Steel Ltd (BPSL), to the RBI.
The company's market valuation also fell by Rs 625.96 crore to Rs 1,522.04 crore on the BSE.
After swinging 327 points during the day, Sensex settled 160.48 points or 0.41 per cent higher at 38,896.71.
The scrip declined 4.17 per cent to Rs 1,300 on the BSE.
The Infosys scrip rose by 6.15 per cent to Rs 771.85 on the BSE.