Option Pricing, Greeks and Volatility
What this domain tests
Pricing questions test whether you can separate intrinsic value from time value, apply put–call parity, and interpret delta, gamma, theta, vega and rho. Volatility questions test implied versus historical volatility and the effect of IV changes on option prices.
Core rules
- European put–call parity with no dividends: C − P = S − K e^(−rT). A violation creates arbitrage.
- Black–Scholes assumes European exercise, lognormal returns, constant volatility and no early exercise; American options need a binomial or similar model because early exercise may be optimal.
- Delta: call 0 to +1, put −1 to 0; approximates change in premium for a ₹1 move. Gamma is the change in delta and is highest near ATM. Theta is usually negative for long options. Vega is positive for long calls and long puts. Rho is positive for calls, negative for puts.
- Implied volatility is the market's forward-looking volatility embedded in price. Higher IV raises both call and put premiums. The volatility smile/skew shows that IV varies by strike.
Worked example
A non-dividend stock is at ₹100, the ₹100 strike has 30 days to expiry and the risk-free rate is assumed zero. A call trades at ₹5 and a put at ₹5. Parity says C − P = 100 − 100 = 0, and 5 − 5 = 0, so prices are consistent. If the call rises to ₹7 while the put stays at ₹5, C − P = 2, above the parity value. A trader could sell the call, buy the put and buy the stock, locking in ₹2 per share before costs. At expiry the stock leg plus put protects the downside, while the short call caps upside; the ₹2 is the arbitrage profit.
Traps
- Applying put–call parity to American options without adjusting for early exercise.
- Assuming higher volatility raises only calls; it raises both calls and puts.
- Confusing delta (price sensitivity) with gamma (delta sensitivity).