Maths in economics, finance and society · Ambitious · Dissertation

Pricing an option with probability: a maths EPQ idea

Why it works as an EPQ

The binomial model prices an option with A Level probability and one clever idea (replication), and lets you test its assumptions.

Scope and difficulty

Ambitious. Ambitious. Stay with binomial trees; mention the continuous model only in the conclusion.

The maths

Builds on these A Level topics: Probability · Statistical distributions · Exponentials and logarithms.

You would learn:

• No-arbitrage pricing
• Risk-neutral probability
• Binomial trees

Learning maths beyond the course is expected in a maths EPQ, but you must understand and explain everything you use.

One possible plan

1. Price a one-step option by building a replicating portfolio.
2. Extend to many steps and compute prices.
3. See how the price changes with volatility and time.
4. Judge the model's assumptions against real markets.

Pitfalls

• Treating risk-neutral probabilities as real ones.
• Advice about investing.

Where to start reading

• Search for: binomial option pricing model one step replication
• Search for: risk neutral valuation explained

Prefer books, lecture notes, journal articles and official data to a single website, and record every source as you read (how to reference).

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All maths in economics, finance and society ideas · all 93 ideas

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