doesnt make any sense. huge difference between call and put implied volatility. May 65 call IV is 56 while May 65 put IV is 89... but that sucker is on fire still call IV is lower then put IV...
this is normal. just take a lot at spx IV for puts vs calls. puts are always higher b/c there is a permanent base of investors who want to hedge which supports IV and also sell covered calls which depresses IV.
The model used to price is probably not pricing borrow correctly. the stock might be really hard to borrow and a result the puts are more expensive to account for the lack of hedging ability.
For the same strike and maturity, the implied vol should be the same. I bet the model you are using doesn't account for borrow. The stock might be hard to borrow and so the price of puts is higher to account for the higher cost of borrow. JK