How LSM Works (without the math headache)

What is LSM?

Least-Squares Monte Carlo (LSM) is the go-to method for valuing American and Bermudan options in energy projects. Unlike European options that can only be exercised at expiration, American options can be exercised anytime, and Bermudan options at specific dates. This flexibility is exactly what makes energy investments valuable — you can "wait and see" how markets develop.

The Key Insight

LSM solves the fundamental question: "At any point in time, should I exercise my option now or wait for potentially better conditions?" This mirrors real investment decisions like "Should we build the battery storage facility this year or wait?"

The Intuition Behind LSM

Think of LSM as a sophisticated decision tree that works backwards through time. Here's the intuitive process:

Simulate thousands of possible futures — What could electricity prices, demand, and regulations look like over the next 10 years?
Start at the end and work backwards — At expiration, the decision is easy: exercise if it's profitable
For each earlier decision point — Compare immediate exercise value vs. expected value from waiting
Use regression to estimate continuation value — This is the "least-squares" part — fit a curve through the data

[DIAGRAM: Decision tree showing backward induction process with price paths and exercise boundaries]

Why Not Just Use Black-Scholes?

Black-Scholes works brilliantly for European options but fails for American options because:

No closed-form solution exists for most American options
Early exercise is path-dependent — the optimal strategy depends on how you got to the current state
Multiple factors matter — electricity prices, demand, regulatory changes all interact

Real World Example: Battery Storage Project

The Scenario

You're evaluating a 100 MWh battery storage facility. Construction takes 18 months, but you have the option to delay the start by up to 3 years based on market conditions. This is a classic Bermudan option with exercise dates every 6 months.

Key Variables:

Electricity price spreads (day/night arbitrage)
Grid services revenue (frequency regulation)
Construction costs (learning curve effects)
Regulatory incentives (time-limited)

Step 1: Generate Price Scenarios

We simulate 10,000 paths for electricity prices using a mean-reverting Ornstein-Uhlenbeck process (because electricity prices don't follow random walks — they tend to revert to fundamental costs).

[CHART: Sample electricity price paths over 5 years showing mean reversion and volatility]

Step 2: Define Exercise Values

At each potential exercise date (every 6 months), we calculate the NPV if we start construction immediately:

Exercise Value = NPV(Revenue Streams) - Construction Cost - Development Cost
                
Where Revenue Streams include:
- Energy arbitrage (buy low, sell high)
- Ancillary services (grid balancing)
- Capacity payments (grid reliability)

Step 3: Work Backwards (The LSM Magic)

Starting from the final exercise date and working backwards:

At expiration (Year 3) — Exercise if NPV > 0, otherwise abandon
At Year 2.5 — For each scenario, compare:
- Exercise now: Immediate NPV
- Wait: Expected value from continuation (estimated via regression)
Continue backwards until we reach today

The Regression Step

This is where "least-squares" comes in. We regress the continuation values against current state variables (price levels, volatility, time to expiration) to create a smooth estimate of "wait value" for any scenario.

Implementation Steps

1. Model Setup

State Variables: Electricity prices, demand growth, regulation scores
Exercise Dates: Every 6 months for 3 years (7 decision points)
Scenarios: 10,000 Monte Carlo paths

2. Payoff Functions

def exercise_value(price_scenario, exercise_date):
    construction_start = exercise_date
    operation_start = construction_start + 18  # months
    
    revenues = calculate_battery_revenues(
        price_scenario[operation_start:], 
        capacity_mwh=100
    )
    costs = construction_cost + financing_cost
    
    return npv(revenues - costs, discount_rate)

3. Backward Induction with Regression

[FLOWCHART: Backward induction process showing regression at each step]

For each exercise date, we:

Identify scenarios where immediate exercise is profitable
For profitable scenarios, regress continuation values against state variables
Compare immediate exercise vs. fitted continuation value
Update the exercise strategy

Common Pitfalls (And How to Avoid Them)

1. Insufficient Scenarios

Problem

Using too few Monte Carlo paths leads to noisy regression estimates and unreliable exercise boundaries.

Solution

Start with 10,000 paths minimum. Use variance reduction techniques like antithetic variates to improve efficiency.

2. Wrong Basis Functions

Problem

Poor choice of regression variables leads to bad continuation value estimates.

Solution

Use economically meaningful variables: current price, recent price changes, time to expiration, volatility measures. Test different polynomial orders.

3. Ignoring Path Dependence

Problem

Exercise decisions often depend on how you reached the current state, not just current values.

Solution

Include path-dependent variables like running averages, maximum/minimum values reached, or time since last regime change.

4. Overfitting the Regression

Problem

Using too many basis functions creates a perfect fit to training data but poor out-of-sample performance.

Solution

Use cross-validation to select the optimal number of basis functions. Keep it economically interpretable.

The Bottom Line

LSM transforms the abstract concept of "flexibility value" into concrete numbers that CFOs and investment committees can understand and trust. By working backwards through realistic scenarios, it captures the true value of "wait and see" strategies that traditional DCF analysis misses entirely.

Real Impact Example

A German utility used LSM to value a wind farm expansion option. Traditional DCF suggested immediate construction (NPV = €12M). LSM revealed the option to wait was worth €28M — more than double — leading them to delay construction by 18 months and capture significantly better feed-in tariff rates.

The key insight: in uncertain markets, the ability to adapt your strategy based on new information is often more valuable than the underlying project itself. LSM quantifies this insight with mathematical rigor while remaining intuitively understandable to decision-makers.