Rupeezy shows a single implied volatility (IV) for the call and the put at the same strike and expiry: it takes the IV of the out-of-the-money (OTM) option and uses it for both. Using two different IVs would break put-call parity.
Why should a call and a put have the same IV?
Put-call parity ties a call and a put with the same expiry and the same strike together, so in an efficient market their IVs should be the same. Across different strikes, IVs usually differ in practice (the "volatility smile"), even though the basic Black-Scholes model assumes a single volatility.
Why doesn't this always hold in India?
- The Securities Transaction Tax (STT) affects in-the-money (ITM) options and brings down their volatility.
- Wide bid-ask spreads make the market less efficient.
This is also why NSE's option chain can show different IVs for a call and a put — see Why is there a difference between NSE's IV and Rupeezy's IV?
How does put-call parity decide which IV to use?
Put-call parity ties the two prices together. In the simplified form that ignores interest — the same assumption Rupeezy's Greeks model makes — it says Call Price − Put Price = Future Price − Strike Price. If different IVs were used to calculate the call and put prices, this equation wouldn't add up. So Rupeezy uses the IV of the OTM option for both the call and the put. For the model behind this, see Which model is used for Greeks Calculations?