Option prices respond to several inputs. In the Black-Scholes-Merton (BSM) framework, the price of a European option depends on:
- Spot Price (\(S_{spot}\)) \(S_0\) – higher spot prices lift call premiums and lower put premiums.
- Option Strike Price \(K\) – sets the level where the option finishes in or out of the money.
- Time to Expiration \(T\) – more time gives the option value a longer chance to move.
- Implied Volatility (\(IV\)) \(\sigma\) – greater expected movement raises both call and put premiums.
- Risk-free Rate \(r\) – higher interest rates slightly boost calls and depress puts.
Dividends or other carrying costs can modify these inputs by adjusting the underlying’s effective price. Understanding how each variable feeds into BSM helps explain why option premiums change when market conditions shift.