"Markets have already been performing well in India on the back of the notion that a BJP government will move forward more aggressively with investment in energy, infrastructure and overall capex," said Sacha Tihanyi, currency strategist at Scotiabank in Hong Kong, discussing a possible BJP victory in elections next year.
Still, opinion and exit polls have a patchy track record in India. Most surveys forecast the wrong outcome in the 2004 general election.
The rupee rose to as high as 61.52 against the dollar, its strongest level since Oct 31. It was last trading at 61.56/57 compared to its 62.05/06 close on Wednesday.
The benchmark BSE index rose as much as 2.2 percent to a session high of 21,165.60 points, approaching a record high of 21,321.53 points hit on Nov. 3.
(Read more: Despite hiccup, rupee recovery likely to continue)
The strong showing bucked the trend in Asian shares, which continued to be hit by worries of an early drawdown of U.S. stimulus.
Indian markets have steadily recovered ground since a volatile summer that saw the rupee hit a record low against the dollar when fears of an early Fed tapering first surfaced.
Measures taken by India's central bank and the ruling Congress Party have been seen as having helped that recovery.
Economic data has also turned more favourable, with data this week showing the current account deficit narrowed to 1.2 percent of gross domestic product, the smallest deficit since the June quarter of 2009.
(Read more: India to tick with austerity despite looming election)
Nonetheless investors see a BJP victory as potentially being more beneficial to markets.
"Based on our discussions with investors, markets are positively inclined towards Mr. Narendra Modi led BJP and less so towards Congress, despite some course correction in policies recently by the latter," UBS said in a 2014 outlook note to clients on Wednesday.