Financial mathematics tutoring: from the binomial model to Black-Scholes

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Financial mathematics brings together probability, analysis and a bit of financial intuition. I help you understand the model before you use the formulas, so you can also handle the question that differs slightly from the example.

What we work through

Probability for finance

  • Conditional expectation
  • Martingales
  • Normal distribution and lognormal prices

Binomial model

  • No arbitrage and the replicating portfolio
  • Risk-neutral probability
  • Multi-period model and American options

Brownian motion and Itô

  • Wiener process and quadratic variation
  • Stochastic integrals
  • Itô lemma and geometric Brownian motion

Black-Scholes

  • The PDE and the formula
  • Change of measure and Girsanov
  • Greeks and hedging

Which courses?

  • UvA BSc Actuarial Science, e.g. a financial mathematics course
  • UvA BSc Econometrics & Data Science, e.g. Financial Mathematics
  • VU BSc Econometrics & Operations Research, e.g. Stochastic Processes or Financial Mathematics
  • UvA/VU MSc Stochastics & Financial Mathematics, e.g. Stochastic Calculus

These are examples (e.g.). Course names and content change from year to year, so check your own study guide. Send me your course and I will look at what you need.

Where it often goes wrong

The risk-neutral q is not the real probability p

q is a pricing device that follows from no-arbitrage. Use q for prices and p for statements about what will actually happen.

d(W²) = 2W dW + dt

Itô adds an extra dt term because W has quadratic variation. The ordinary chain rule gives 2W dW and misses it.

The discounted price is a martingale under q

The price itself is not: it drifts with the interest rate. Forget the discounting and your expectation is off.

What does it cost?

  • I teach this subject myself: €300 online or €400 on location per 4-hour package, 1 student.

Two or more students can pay less per person, see the price table on the contact page.

Want to see if I can help?

Send me a message with your course and when your exam is. I reply myself.