workflow-derivatives-real-options

# Real Options Valuation ## What this skill covers A structured pipeline for quantifying the value of managerial flexibility embedded in capital investment decisions. Real options are priced using the CRR binomial tree via `real_option_valuation`, supplemented by decision-tree rollback and expected-value calculations via `decision_tree_analysis`. The analysis produces the real-option value (ROV), the static NPV, the option premium (ROV minus NPV), and the optimal exercise threshold. Apply this workflow when project volatility exceeds 30% or when the capital decision involves irreversibility, staging, or contingency on future outcomes. ## Workflow ### Phase 1 — Static NPV Baseline 1. Establish the static (no-flexibility) NPV as the baseline: - Call `dcf_model` or `monte_carlo_dcf` with the project's base-case cash flow projections, WACC, and terminal value assumptions. - Record the static NPV. A negative or marginal static NPV does not preclude a positive real-option value. 2. Call `wacc_calculator` to confirm the discount rate, or document the hurdle rate if the project uses a project-specific risk adjustment. 3. Document the investment cost (I), the underlying project asset value (V₀ = PV of future cash inflows without flexibility), and the ratio V₀/I (analog to S/K for an option): - V₀/I < 0.8: deep out-of-the-money; option value is primarily from vol premium. - V₀/I 0.8–1.2: at-the-money; flexibility has the highest marginal value. - V₀/I > 1.2: in-the-money; deferral option has less value but abandonment may still matter. ### Phase 2 — Project Volatility Estimation 4. Estimate project-specific volatility (σ) using one or more of the following approaches: - **Comparable public company vol**: pull `fmp_historical_price` for 3-5 comparable companies and compute annualized realized vol. Average or median serves as the project vol proxy. - **Management range**: if management provides optimistic and pessimistic V₀ estimates, compute σ = (ln(V_high / V_low)) / (2 × 1.65 × sqrt(T)) for a 90th-percentile range. - **Monte Carlo vol**: run `monte_carlo_dcf` and compute the standard deviation of the NPV distribution, then express as a fraction of V₀. 5. Flag if σ < 15% (real option adds little) or σ > 60% (binomial tree may require more steps for accuracy; use ≥ 500 steps). ### Phase 3 — Real Option Valuation 6. Call `real_option_valuation` with: - `option_type`: one of `"defer"`, `"abandon"`, `"expand"`, `"contract"`, `"switch"`, or `"compound"`. - `asset_value` (V₀): PV of cash inflows without flexibility (from Phase 1). - `investment_cost` (I): capex or exercise price. - `volatility` (σ): from Phase 2. - `risk_free_rate`: from `fmp_treasury_rates` at the option tenor. - `tenor`: time until the option expires (years the decision can be deferred, or project life for abandonment). - `steps`: minimum 200; use 500 for high-volatility projects. - `dividends`: any cash outflow from holding the project (maintenance, opportunity cost as % of V₀ per year). 7. Extract from the tool response: - **Real option value (ROV)**: binomial-tree option price. - **Option premium**: ROV minus max(static NPV, 0). This is the value of flexibility. - **Optimal exercise threshold**: the minimum V₀ at which immediate exercise is optimal (analogous to the early-exercise boundary for American options). ### Phase 4 — Decision Tree Analysis 8. For staged or contingent investments, construct an explicit decision tree and call `decision_tree_analysis`: - Define decision nodes (invest / wait / abandon) and chance nodes (market outcomes: favorable / unfavorable). - Assign probabilities and payoffs to each branch from analyst assumptions or scenario model. - The tool returns: EMV (expected monetary value) at each node, optimal decision path, and EVPI (expected value of perfect information). 9. Compare EMV from the decision tree to the binomial ROV. Material divergence (> 15%) indicates that the decision tree's discrete branching does not adequately capture continuous price dynamics; the binomial ROV is preferred in that case. ### Phase 5 — Sensitivity Analysis 10. Call `sensitivity_matrix` with project volatility (σ) on one axis (±10, ±20, ±30% of the base estimate) and V₀/I ratio on the other axis (0.6, 0.8, 1.0, 1.2, 1.4) to produce a 5 × 5 ROV grid. 11. Call `scenario_analysis` with: - **Bear**: low V₀, high I, low σ. - **Base**: central estimates. - **Bull**: high V₀, low I, high σ. - Report ROV and option premium in each scenario. ### Phase 6 — Strategic Interpretation 12. Interpret the real option analysis for the capital decision: - **Defer**: is waiting valuable? Compare ROV to static NPV. If ROV > I and static NPV < 0, the project creates value only through the deferral option. - **Abandon**: does the abandonment option justify proceeding? If salvage value × probability of abandonment > 10% of project cost, the option is material. - **Expand/contract**: quantify the percentage uplift or downside mitigation from scale flexibility. - **Compound**: for staged investments, each stage is an option on the next; document the option-on-option structure. ## Output Format ### Static NPV Baseline | Parameter | Value | Source | |---|---|---| | PV of cash inflows (V₀) | — | `dcf_model` / `monte_carlo_dcf` | | Investment cost (I) | — | Input | | Static NPV | — | `dcf_model` | | V₀ / I ratio | — | Computed | | WACC / hurdle rate | — | `wacc_calculator` | ### Project Volatility | Method | Estimated σ | Source | |---|---|---| | Comparable company realized vol | — | `fmp_historical_price` | | Management range estimate | — | Analyst assumption | | Monte Carlo NPV distribution | — | `monte_carlo_dcf` | | **Selected σ** | — | Basis for ROV | ### Real Option Valuation | Parameter | Value | Source | |---|---|---| | Option type | — | Input | | Asset value (V₀) | — | Phase 1 | | Investment cost (I) | — | Input | | Volatility (σ) | — | Phase 2 | | Risk-free rate | — | `fmp_treasury_rates` | | Option tenor (years) | — | Input | | Binomial steps | — | Input | | **Real option value (ROV)** | — | `real_option_valuation` | | Static NPV | — | `dcf_model` | | **Option premium (ROV − NPV)** | — | Computed | | Optimal exercise threshold (V₀*) | — | `real_option_valuation` | | Option premium as % of V₀ | — | Computed | ### Decision Tree Summary (if applicable) | Node | Decision / Outcome | Probability | Payoff | EMV | |---|---|---|---|---| | Metric | Value | Source | |---|---|---| | EVPI | — | `decision_tree_analysis` | | Optimal path | — | `decision_tree_analysis` | ### Scenario Analysis | Scenario | V₀ | I | σ | ROV | Option Premium | |---|---|---|---|---|---| | Bear | — | — | — | — | — | | Base | — | — | — | — | — | | Bull | — | — | — | — | — | ### Sensitivity Matrix: ROV vs Volatility and V₀/I (5 × 5 grid — output from `sensitivity_matrix`) ### Strategic Recommendation | Option type | Current status | Recommendation | |---|---|---| ### Tool-Call Traceability | # | Tool | Key Inputs | Output | |---|---|---|---| ## Quality Gates - [ ] Static NPV baseline established via `dcf_model` or `monte_carlo_dcf` before calling `real_option_valuation`. - [ ] Project volatility estimated from at least one data-driven method using `fmp_historical_price` or `monte_carlo_dcf`; not assumed arbitrarily. - [ ] `real_option_valuation` called with correct option type matching the decision being analyzed. - [ ] Binomial steps ≥ 200; increased to ≥ 500 if σ > 60%. - [ ] Option premium documented as ROV minus max(static NPV, 0) and as % of V₀. - [ ] Optimal exercise threshold (V₀*) reported and interpreted. - [ ] Decision tree (`decision_tree_analysis`) used for staged / contingent structures; EVPI reported. - [ ] Sensitivity matrix produced: σ range × V₀/I range. - [ ] Scenario analysis present: bear, base, bull with probability weights summing to 100%. - [ ] Real option premium benchmark check: 10-30% of static NPV is the expected range; deviations documented. - [ ] Every number in output maps to a row in the traceability table. ## Related Skills - `workflow-derivatives-option-pricing` — real options share the binomial tree pricing engine; vanilla option concepts apply. - `workflow-derivatives-futures-forwards` — deferral options on commodity projects require forward curve inputs for V₀ estimation. - `corp-finance-analyst-derivatives` — agent body with real-option type definitions and CRR binomial conventions. - `corp-finance-analyst-core` — DCF and WACC methodology for the static NPV baseline.