In traditional finance, valuation often begins with the discounted cash flow (DCF) model—a tool designed to estimate the value of an asset by forecasting its future cash flows and discounting them back to today using a suitable discount rate. It’s a bedrock technique for valuing businesses, bonds, and income-generating properties.

But try using DCF to price a stock option and you’ll quickly run into a wall.

Why the DCF Model Fails for Options

At a glance, it might seem reasonable to project an option’s potential payoff and discount it at the risk-free rate. But options are not like shares or bonds. They have unique characteristics that break the assumptions that underpin the DCF model.

Here’s why the model doesn’t work:

1. Options Have Asymmetric, Nonlinear Payoffs

Unlike the predictable, linearly accruing payments of dividends or bond coupons, options have asymmetric and conditional payoffs. A call option, for instance, only pays off if the stock ends above the strike price. If it expires out-of-the-money, the payoff is zero. This discontinuity isn’t something the DCF model handles well.

2. Cash Flows Are Uncertain and Often Zero

Options don’t produce steady cash flows. In fact, the cash flow may be nothing at all if the option expires worthless. And even when there is a payoff, the timing and amount depend entirely on market movements—which the DCF model assumes are predictable or at least estimable.

3. Volatility Is Central to Value

DCF models ignore volatility, but for options, volatility is critical. The more volatile the underlying asset, the more valuable the option—even if the expected return of the asset doesn’t change. That’s because higher volatility increases the likelihood of extreme outcomes and options profit from such moves.

4. Risk-Neutral Valuation vs Discount Rates

The DCF model uses a risk-adjusted discount rate based on the investor’s required return. In contrast, modern option pricing uses risk-neutral valuation, which adjusts probabilities rather than discount rates. Under this framework, you compute the expected payoff assuming all assets earn the risk-free rate, and then discount at that same rate.

5. Options Are Valued Probabilistically

DCF is a deterministic model. It doesn’t account for the probabilistic range of outcomes that options are sensitive to. Option valuation requires modelling the distribution of potential prices, not just their expected value.

The Black-Scholes-Merton Breakthrough

In 1973, economists Fischer Black, Myron Scholes, and Robert Merton introduced what would become the most influential model in financial derivatives: the Black-Scholes-Merton (BSM) model. Their goal? To find a rational, market-consistent way to value European-style options—those that can only be exercised at expiry.

Rather than projecting cash flows, they approached the problem from a radically different angle: hedging and replication.

Step-by-Step Intuition:

Model the Stock as a Stochastic Process
They began by modelling the stock price as a random, continuous process, following a lognormal distribution. Prices could go up or down in infinitesimal steps, and their changes were proportional to the current price and driven by volatility.
Construct a Riskless Portfolio
If you hold one option and take an offsetting position in the underlying stock—specifically, a dynamically adjusted quantity—you can create a hedged portfolio. This setup eliminates risk for a very short period, making the portfolio effectively risk-free.
Apply No-Arbitrage Logic
Since this hedged portfolio is riskless, it must earn the risk-free rate. If not, arbitrageurs could profit with zero risk, which would contradict market efficiency. This logic leads to a partial differential equation that can be solved to yield the option’s fair value.
Solve for the Option Price
The end result is a closed-form formula that determines the value of a European call or put option based on five observable variables:
- The current price of the underlying asset
- The option’s strike price
- Time to expiry
- The risk-free interest rate
- The volatility of the underlying asset

Assumptions of the Model

Whilst the BSM model was ground-breaking, it rests on some simplifying assumptions:

Despite these, the model’s analytical elegance and practical accuracy made it the standard for options pricing—especially as computers allowed faster, real-time recalculations and sensitivity analysis.

The Greeks and Beyond

One of the model’s most powerful contributions is the ability to calculate the Greeks—sensitivities of an option’s value to various inputs:

Delta: how much the option price changes with the underlying
Vega: sensitivity to volatility
Theta: time decay
Gamma: rate of change of delta
Rho: sensitivity to interest rates

These metrics allow traders and risk managers to hedge and monitor exposures precisely.

Legacy and Impact

The Black-Scholes-Merton model didn’t just change how options are priced—it helped launch the modern derivatives industry. Exchanges like the Chicago Board Options Exchange (CBOE) flourished, and academic finance found new rigour.

In 1997, Scholes and Merton were awarded the Nobel Prize in Economic Sciences. (Fischer Black had passed away in 1995 and was ineligible posthumously.)

Final Thoughts

The DCF model may remain the go-to method for valuing companies, bonds, and income-producing assets. But when it comes to options—assets that are conditional, volatile, and path-dependent—it falls short.

The Black-Scholes-Merton framework ushered in a new era of probabilistic, risk-neutral pricing, better suited to the complexities of modern markets. And whilst it’s far from perfect, it’s still the backbone of derivatives pricing and financial engineering to this day.

References

Black, Fischer, and Myron Scholes. 1973. ‘The Pricing of Options and Corporate Liabilities.’ Journal of Political Economy 81 (3): 637–654.

Khan, Sal. 2013. Introduction to the Black-Scholes Formula. YouTube video, 10:23. Posted July 2013. https://www.youtube.com/watch?v=pr-u4LCFYEY

Merton, Robert C. 1973. ‘Theory of Rational Option Pricing.’ The Bell Journal of Economics and Management Science 4 (1): 141–183.

Why the DCF Model Doesn’t Work for Options—and How Black-Scholes-Merton Changed Everything