# Options Structures and Scenario Analysis Describe nonlinear option exposure across price, time and volatility scenarios. Use this workbook alongside the course. Write your answers before opening the solutions. Practical work is self-reviewed; scored knowledge checks are in the Academy. ## 1. Payoff foundations ### Calls and puts A call and put have different payoff directions under their contract terms. For simplified expiry examples, call payoff is max(underlying minus strike, zero), while put payoff reverses that difference. Premium and multiplier are added separately to profit calculations. ### Long versus short premium Long premium pays for contractual rights; short premium accepts obligations in exchange for premium. Receiving cash at entry does not establish profit, because the later liability can exceed the initial receipt. ### Intrinsic and time value Intrinsic value is the positive immediate exercise component in a simplified model. Time value and other pricing effects matter before expiry. A position's current market value cannot generally be read from its expiry payoff alone. ### Expiry payoff versus mark-to-market Distinguish payoff from profit. Profit includes premium, fees and the actual closing or settlement terms. A diagram that omits the initial premium can make a losing position appear profitable. ### Worked example A put with strike 100 expires at underlying 94. Payoff is 6. If premium was 4 and multiplier one, profit is 2 before costs. At underlying 99, payoff is 1 and profit is −3. ### Independent exercise Calculate the expiry profit of the same purchased put when the underlying is 105. Explain the role of premium. My inputs and assumptions: My calculation or decision: Evidence that would change my conclusion: ## 2. Structures ### Vertical spreads A vertical spread combines options of the same type and expiry at different strikes. For a simple debit call spread, the purchased lower-strike call is offset by a sold higher-strike call. State the net premium and equal contract units. ### Protective options Protective options are evaluated alongside the exposure they are intended to modify. The protection may involve premium cost, basis differences and expiry mismatch. A hedge label does not eliminate these trade-offs. ### Covered positions Covered positions pair an option obligation with another holding, but coverage depends on quantity, underlying and contractual treatment. The combined position can still lose substantially; covered does not mean risk-free. ### Calendar exposure concepts Calendar structures combine expiries and therefore involve different time and volatility sensitivities. A terminal payoff at one expiry may leave another option open. Do not collapse the structure into a single-expiry diagram without explaining the remaining leg. ### Worked example Buy a 100 call and sell a 110 call for net debit 4, equal units. At expiry reference 108, spread payoff is 8 and profit 4. At 115, payoff is capped at 10 and profit 6 before costs. ### Independent exercise Calculate the spread's expiry profit at 95 and at 103. Identify the maximum loss in this simplified fully matched expiry example. My inputs and assumptions: My calculation or decision: Evidence that would change my conclusion: ## 3. Risk drivers ### 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. ### Independent exercise Explain why a scenario table should include repricing rather than only initial delta times a large price move. My inputs and assumptions: My calculation or decision: Evidence that would change my conclusion: ## 4. Decision analysis ### Breakeven assumptions Breakeven calculations depend on premium and costs under a particular horizon. Expiry breakeven is not necessarily the price at which the position can be closed without loss before expiry. ### Adverse volatility changes Adverse volatility changes can offset a favorable underlying move. Scenario analysis should vary both and consider time passage. A directional thesis alone is incomplete for a nonlinear position. ### Early exit valuation Early exit valuation uses current executable prices or a clearly labelled model, not simply the final payoff formula. Remaining time value can make the result differ substantially from an expiry diagram. ### When a payoff diagram is insufficient A payoff diagram omits funding, execution and operational path. Use it to understand one terminal relationship, then supplement it with scenario and cash-flow analysis before judging feasibility. ### Worked example A purchased call's underlying rises slightly, but implied volatility falls sharply and time passes. The option can still lose value before expiry. The direction of the underlying alone cannot determine the mark-to-market result. ### Independent exercise Create a three-scenario worksheet varying underlying, volatility and time. State what source or model would be used for each option value. My inputs and assumptions: My calculation or decision: Evidence that would change my conclusion: ## Course project Produce payoff and scenario tables for a defined-risk illustrative spread. ### Self-review rubric - Concepts and reasoning: 25% - Calculations, data and evidence: 30% - Process and risk controls: 25% - Limitations and communication: 20% Record one correction and one next practice task. This rubric is not automatically graded. ## Worked solutions ### Exercise 1 The put expires with zero intrinsic payoff under the simplified terms, so profit is −4 before costs. The premium paid is a cost even when no exercise value remains. ### Exercise 2 At 95, both calls have zero payoff and profit is −4. At 103, payoff is 3 and profit is −1. The net debit 4 is the maximum terminal loss under the simplified matched-contract assumptions, before costs and operational complications. ### Exercise 3 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. ### Exercise 4 The worksheet should label executable quotes separately from model estimates, include costs and show all changed inputs. It should not claim a precise fill merely because the model produces a precise number. ## Further reading - https://www.cmegroup.com/education - https://www.investor.gov/introduction-investing