According to Black Scholes theory and in practical efficient markets,
- IV for call and put options for the same expiry and same strike price should be the same
- IV for call and put options for the same expiry and different strike price should be different
However, this is not always true in India because:
- Securities Transaction Tax affects ITM options and brings down volatility
- Inefficiency due to wide bid-ask spreads
Put Call Parity says that Call Price - Put Price = Future Price - Strike Price. If we use different IVs in call and put price calculation, this equation will not add up. So, we use the IV of the OTM option and use it for both Put and Call option.