Law of One Price and Replication
Two things with identical payoffs in every state must have the same price.
That is the whole of derivatives pricing theory. Everything else is working out what replicates what.
Why it holds
If two identical payoffs had different prices, you would buy the cheap one, sell the expensive one, and hold a position with zero payoff in every future state and positive cash today. Free money, taken in unlimited size until the prices converged.
The force is not that markets are wise; it is that the alternative is exploitable.
Pricing by replication
The consequence is a method. To price a derivative, build a portfolio of tradeable assets that reproduces its payoff in every state, and the derivative must cost what the portfolio costs.
The binomial example shows it concretely: a call is replicated by shares plus borrowing, and its price is the cost of that package.
The rest of this lesson is for subscribers
Unlock every lesson in Basics of Quantitative Finance, and every other premium course.
Subscribe to continueTest your knowledge
Keep reading Basics of Quantitative Finance
23 lessons in this course, and every other premium course, on one subscription.
- Every lesson in every course, with the worked examples and interactive simulators
- Graded questions on every lesson, with explanations for the wrong answers as well as the right one
- The trainers, timed assessments and brainteaser library that go with them