Conditional Expectation Explained

Описание: In this video, we explore conditional expectation in the context of the binomial pricing model — a foundational concept in financial mathematics and derivative pricing. Starting from risk-neutral probabilities and partial coin toss histories, we build up the intuition and formal definition of conditional expectation step by step.
You’ll learn how to interpret conditional expectations based on what we know so far, and how to average over the two possible outcomes at the next time step using risk-neutral probabilities. We also introduce the general definition over all possible continuations and explain what a “continuation” means in simple terms.
Along the way, we walk through the key properties that make conditional expectation such a powerful tool — including linearity, iterated conditioning, and conditional Jensen’s inequality. These ideas are essential for understanding fair pricing, hedging, and the structure of financial models.
This video sets the stage for martingales, which we’ll cover next — showing how conditional expectation connects to fair games and risk-neutral valuation.

🎯 Ideal for:
CFA candidates
Finance and economics students
Quantitative analysts
Anyone curious about the math behind derivatives
📚 Topics covered:
Risk-neutral probabilities and coin toss modeling
Conditional vs unconditional expectation
Continuations and partial information
Step-by-step breakdown of conditional expectation
Key properties and intuition
Jensen’s inequality (conditional version)

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#FinanceEducation #ConditionalExpectation #BinomialModel #CFAprep #QuantitativeFinance #RiskNeutralPricing