WHAT: Apply real-option valuation to corporate capital allocation decisions (defer, abandon, expand, contract, switch); use binomial tree pricing and decision-tree rollback to quantify the option premium over static NPV.
WHEN: Invoke for capex deferral analysis, project abandonment value, growth-option strategic valuation, staged investment sequencing, or any capital decision where managerial flexibility has material value.
インストール
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WHAT: Apply real-option valuation to corporate capital allocation decisions (defer, abandon, expand, contract, switch); use binomial tree pricing and decision-tree rollback to quantify the option premium over static NPV.
WHEN: Invoke for capex deferral analysis, project abandonment value, growth-option strategic valuation, staged investment sequencing, or any capital decision where managerial flexibility has material value.
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
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.
Call wacc_calculator to confirm the discount rate, or document the hurdle rate if the project uses a project-specific risk adjustment.
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
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.
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
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).
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
For staged or contingent investments, construct an explicit decision tree and call decision_tree_analysis:
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).
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
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.
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
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.
