What you will learn
- Delta and gamma
- Vega and theta
- Liquidity and spread costs
- Exercise and assignment terms
Delta and gamma
Delta approximates sensitivity to a small underlying-price move, while gamma describes how that sensitivity changes. These are local model quantities, not fixed multipliers valid for every shock.
Vega and theta
Vega describes sensitivity to the model's volatility input; theta describes passage-of-time effects under a convention. Their signs and magnitudes depend on the position. Varying one input while freezing all others is an approximation.
Liquidity and spread costs
Liquidity and spreads affect whether model values can be realized. Multi-leg positions incur execution costs across legs, and wide markets can make apparent theoretical gains unavailable.
Exercise and assignment terms
Exercise and assignment follow contract-specific rules. Early exercise eligibility, settlement style and resulting positions can create obligations different from the intended diagram. Verify terms and account handling before applying a generic strategy description.
Worked example
A local delta estimate predicts a small gain for a small move, but a large shock changes delta materially. Applying the initial delta linearly to the entire shock ignores gamma and potentially other changing inputs.
Try it yourself
Explain why a scenario table should include repricing rather than only initial delta times a large price move.
Show the worked solution
Repricing can account for changing sensitivities, volatility and time assumptions. It remains model-dependent, but it is more informative than treating a local derivative as globally constant across a large shock.
Apply this to your course project
Produce payoff and scenario tables for a defined-risk illustrative spread.
Keep the calculation inputs, assumptions and decisions with your work. Practical exercises are self-reviewed; the scored knowledge checks assess the questions shown, not an independent certification of practical competence.