EFN507 Chap.11 Real Options and Binomial Option Pricing
Real Options and Binomial Option Pricing
Flexibility as an option
Weeks 9 and 10 turn to real options: the rights to expand, delay or abandon a project that static NPV ignores. Each is valued like a financial option, because it lets the firm keep good outcomes and avoid bad ones.
The teaching plan lists financial options, real options and binomial option pricing, and the lecture materials note the unit derives the binomial formula rather than simply using it.
The binomial tree
The formula sheet gives the risk-neutral probability, the one-step option value and the up factor from volatility, along with the Black and Scholes call formula with a dividend yield.
A two-step tree is valued by working backwards from the final payoffs, checking at each node whether exercising early beats waiting. Survey evidence in the unit shows such methods are known but used by a minority of Australian firms.
What this chapter covers
- 01
Options to expand, delay and abandon
- 02
Replication and risk-neutral probabilities
- 03
One-step and two-step binomial valuation
- 04
Early exercise and backward induction
- 05
Black and Scholes with a dividend yield
- 06
How common real options are in practice
Worked example · free
The option to abandon on a two-step tree
- +2u = e^(0.3 × √0.5) = 1.2363, d = 0.8089 and q = (e^0.025 − 0.8089) ÷ (1.2363 − 0.8089) = 0.5064.
- +1Final project values are 152.85, 100.00 and 65.43, so the payoffs are $0, $0 and 90 − 65.43 = $24.57m.
- +2Down node: (0.4936 × 24.57) × e^−0.025 = $11.83m, more than abandoning at once for $9.11m.
- +1Today: (0.4936 × 11.83) × e^−0.025 = $5.70m.
Key terms
- Real option
- A right, but not an obligation, to change a real investment, such as expanding, delaying or abandoning it.
- Binomial tree
- A lattice in which an asset's value moves up or down by fixed factors each step, used to value options.
- Backward induction
- Valuing an option by starting at the final payoffs and discounting expected values one step at a time.
- Abandonment option
- The right to stop a project and recover its salvage value, which behaves like a put option.
Real Options and Binomial Option Pricing FAQ
Why does static NPV undervalue flexible projects?
It assumes the firm commits to one path today. A real project lets managers react to news, expanding after good outcomes and stopping after bad ones, and that ability to cut off the downside has value that a single cash flow forecast leaves out.
Why can the option be discounted at the risk-free rate?
Its payoff can be copied with a position in the underlying asset and borrowing. The copy and the option must cost the same, so the option can be priced with risk-neutral weights and the risk-free rate, whatever investors' attitudes to risk.
Is the risk-neutral probability the real chance of an up move?
No. It is the weight that makes the risk-free rate the correct discount rate for the option's payoffs. The real probability is built into the current value of the underlying asset and does not need to be estimated.
How is an abandonment option like a put?
The firm can sell the project for its salvage value, just as a put holder can sell an asset at the exercise price. It pays off when the project value falls below the salvage value, and is worth more when volatility is higher.
What does the dividend yield represent for a real option?
The cash flows the project would produce while the firm waits to invest. Waiting forgoes them, so a higher yield lowers the value of the option to delay and can make investing early the better choice.
How common are real options in practice?
The survey evidence reviewed in the unit shows real options methods used by about a third of responding Australian firms, far fewer than NPV or payback. The tutorial summary describes them as starting to be used but far from common.
Exam move
Build a one-step and a two-step tree by hand from the formula sheet, value one call and one put on each, and check early exercise at every node. Then rework one Black and Scholes call with a dividend yield.
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