For a given option,
– people use Black-Scholes to graph theoretical option price against __underlying_spot_price__. Then they get the gradient – delta
– people use Black-Scholes to graph spot option price against _time_ to expiration. Then they get the gradient – theta.- people use Black-Scholes to plot spot option price against implied _volatility_ for the period to expiry. Then they get the gradient – vega
– people don’t normally plot spot option prices against exercise price (K), although strike price is an important factor.
For short term liquid options, the effect of tweaking the interest rate (like 200bps to 201) is relatively minor. (That gradient is rho.) IR is built into a fwd price. Becomes important for longer-term options