Idea behind pricing by replication
Question
Explain what it means to price a derivative by replication.
Short answer
Find a trading strategy in assets with known prices that reproduces the derivative's payoff in every state; its cost is the derivative's price. If the two differed you could buy the cheap one and sell the dear one for a riskless profit. Replication can be static (put-call parity, call spreads) or dynamic (continuous delta hedging in Black-Scholes); the price then does not depend on investors' risk preferences or the asset's expected return.
Adapted from Joshi, Denson & Downes, Quant Job Interview Questions and Answers, Q2.39, p.20; question and answer rewritten by SelfMadeQuant.com.
See the hint and the full worked solution in the question bank (free account).
Open the worked solutionLessons behind this question
- The Law of One Price and Replication: No-Arbitrage Pricing from First Principles
- The One-Period Binomial Model: Replication, Delta Hedging, and Risk-Neutral Pricing
Start with a free lesson: Options is part of a free topic. Create a free account, no card needed, to read it in full with worked solutions.
Read it free