Fundamentals of Quantitative Finance
Learn the details behind financial modeling and derivatives pricing.
Coming soon
Starts in:
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Course category:
5 days
8 hours/day
Class size:
20 students
A short course providing you with applied mathematical tools for financial markets.

In our extensive five-day training course, you will learn how probability and statistics are applied to answer the most interesting questions in pricing and modeling of financial products.

We'll start by reviewing the necessary mathematical concepts, such as probability and statistics and will work our way through relevant topics in stochastic calculus. These tools and techniques will be then applied to explore the Black-Scholes framework and how it’s used across derivatives pricing. We will conclude with a practical investigation of numerical pricing methods such as Finite Differences and Monte Carlo.

A good understanding of financial markets and basics of Equity or FX derivatives is highly recommended for this course.

What will you learn?
By the end of the course, you will:
  1. Gain a solid understanding of the Black-Scholes framework and its applications within the financial markets.
  2. Refresh your knowledge on statistics, probability theory and Partial Differential Equations (PDEs).
  3. Be able to construct a simple Brownian motion process and become familiar with random process modeling.
  4. Appreciate the notions of complete and arbitrage-free markets and what they mean for asset valuation.
  5. Explore how Finite Difference and Monte Carlo methods are used to value complex financial derivatives.
  6. Understand the relationship between the Binomial model and the Black-Scholes formula.
  7. Be able to derive various risk metric formulas for European vanilla options.
  8. Understand and apply different approaches to volatility modeling and forecasting.
  9. Know how to back out risk-neutral probabilities from listed option prices and construct a probability distribution.
  10. Learn how to amend the Black-Scholes framework to new products and payoffs.
And much more!
Who is the course for?
  • Private traders and investors, looking to learn the specifics behind derivatives pricing.
  • Professionals within financial institutions or those providing services to the financial sector.
  • Technology specialists within the financial industry – software developers, financial engineers, quantitative analysts and desk strategists.
  • Students, considering or preparing for a degree in quantitative or mathematical finance.
  • Anyone looking to understand quantitative finance theories and their applications.
Course Content
Day 1
  1. Review of Mathematical Concepts:
    • Variance and standard deviation.
    • Covariance and correlation.
    • Random variables and expected value.
    • Probability distributions.
    • Law of large numbers and the Central Limit Theorem.
    • Partial Differential Equations (PDEs).
    • Taylor Series expansion.
    • Heat equation.
  2. Review of Financial Derivatives:
    • Futures and forward contracts.
    • Options.
    • Barrier options.
    • Binary and digital options.
    • Asian options.
    • Structured products.
  3. Risk, Reward and Portfolio Theory:
    • Time value of money.
    • Risk-free and risky assets.
    • Diversification and correlation.
    • Markowitz portfolio theory.
    • Efficient frontier.
    • Market price of risk.
    • Utility functions.
    • One-period portfolio optimization.
Day 2
  1. Binomial Asset Pricing Model:
    • One-step binomial model.
    • Risk-neutral probabilities.
    • Extending to multi-step model.
    • Estimating time-steps and asset moves.
    • Risk-neutral pricing.
  2. Stochastic Calculus and Brownian Motion:
    • Constructing a random process.
    • Properties of a Brownian motion.
    • Martingales and martingale property.
    • Stochastic Differential Equations (SDEs).
    • Stochastic Integration.
    • Ito’s lemma.
    • Arithmetic and geometric Brownian motions.
    • Ornstein–Uhlenbeck process.
    • Feyman-Kac formula.
    • Kolmogorov equations.
    • Hitting probabilities and expected exit times.
    • Optional stopping times.
    • Girsanov theorem and a change of measure.
Day 3
  1. Introduction to Black-Scholes Framework:
    • Assumptions of the Black-Scholes model.
    • Risk-neutral pricing.
    • Delta hedging.
    • Deriving the Black-Scholes model.
    • Properties of the Black-Scholes equation.
    • Solving the Black-Scholes equation.
    • Incorporating dividends and pricing FX options.
    • Pricing American options.
  2. Calculating the Greeks:
    • Delta and delta hedging.
    • Gamma and gamma hedging.
    • Volatility and vega.
    • Relationship between gamma and vega.
    • Interest rates and rho.
    • Time and theta.
  3. Exotic Options:
    • Digital and binary options.
    • Quanto options and contracts on foreign assets.
    • Multi-asset options.
    • Asian options.
    • Barrier options and the reflection principle.
    • Lookback options.
Day 4
  1. Fundamental Theorem of Asset Pricing:
    • Arbitrage and arbitrage-free markets.
    • Complete markets.
    • Equivalent martingale measure.
    • Market price of risk.
  2. Volatility Modeling:
    • Measuring volatility.
    • ARCH, GARCH and other econometric models.
    • Deterministic volatility models.
    • Local volatility model and Dupire equation.
    • Stochastic volatility models.
    • Hedging an option in incomplete markets.
    • Heston volatility model.
    • Variance swaps and the VIX index.
  3. Basics of Interest Rate Modeling:
    • Discounting and zero-coupon bond.
    • Relationship between bond prices, spot rates and forward rates.
    • Deriving the PDE for bond prices.
    • Bond risk-free portfolio.
    • Vasicek model.
    • Cox-Ingersoll-Ross model.
Day 5
  1. Calibration of Derivatives Pricing Models:
    • What is calibration?
    • Black-Scholes formula and implied volatility.
    • Risk-neutral probabilities.
    • Breeden-Litzenberger formula.
    • Local volatility.
  2. The Finite-Differences Method:
    • Truncation and grid-specification.
    • Right, left and central difference.
    • Boundary conditions and vanishing gamma.
    • Explicit and Implicit Euler scheme.
    • The Theta method.
    • Crank Nicolson method.
    • Calculating Greeks.
    • Extending to American options.
  3. The Monte-Carlo Method:
    • Comparison with Finite-Difference methods.
    • Generating Normal random variables.
    • Expectation and integration.
    • Improving convergence.
    • Calculating the Greeks.
    • Path-simulation and Euler-Maruyama method.
    • Pricing path-dependent options.
    • Pricing American options using Monte Carlo.
What’s the format?
Dynamic in-class lectures.
Practical assignments and exercises.
Interactive demos and examples.
Challenging quizzes and tests.
Next available dates and pricing:
Fundamentals of Quantitative Finance
  • Course category:
  • Location:
  • Duration:
    5 days
  • Class size:
    20 students
Date to be confirmed
Coming soon
What will you get upon completion?
  • Formal completion certificate.
  • Course notes and materials.
  • Follow-up support – ability to ask questions and seek further clarification, if needed.
  • 20% OFF any future courses you wish to attend.
What our training participants say?
Financial Sales
“As part of a financial training program, Sergei equipped me with the knowledge that I am still benefiting from seven years later. He has an ability to deliver complex subject material in a digestible way.”
Machine Learning Engineer
“Sergei’s lucid explanations helped me get a deeper grasp of the concepts I was grappling with, whilst giving me a new perspective on the material. I credit him with getting me up to speed when I needed it most.”
Financial Sales
“Sergei is a very good teacher, and is able to explain clearly complex concepts. I felt his course was time well spent.”
Quantitative Developer
“Sergei's sessions were great! He always made them engaging and fun.”
Head of Pricing
“Sergei has a dynamic approach to teaching and his ability to breakdown complex commercial concepts makes learning easy and memorable. I still remember his enthusiasm after 7 years and always happy to learn from him.”
Financial Software Engineer
“Sergei taught me statistics in the context of equity asset prices and he managed to help me finally connect the maths to the real life applications of it. He's very practical and effective in helping you understand hard concepts.”
Data Analyst
“Amazing training! Sergei does a great job at explaining the concepts using simple analogies which makes the complex world of finance very clear.”
Software Engineer
“I attended Sergei's derivatives training a few years ago. Sergei clearly explained what they are, the motivation behind them and how they're traded in concrete terms. After the training I had a solid understandings on the topic and I would recommend Sergei's training.”
Financial Software Developer
"An excellent presenter and an enjoyable course, complex material presented in an approachable fashion."
Investment Professional
“Sergei is one of the best instructors I have ever met. He understands people learn in different ways and can adjust his teaching style. I would highly recommend him, especially when you are trying to learn something complicated or you want to learn something quickly.”
Account Executive
“Sergei held one of the best training sessions on equity derivatives at the onset of my career in finance. He was able to put together a fully comprehensive and detailed yet digestible programme. His strength is delivering complex concepts in a simplified and engaging manner.”
Accounts Manager
“Sergei led various financial trainings and I really enjoyed his teaching style and dedication to his students. He always made sure students were engaged and understood the topic before moving on. I would recommend Sergei for his professionalism and deep knowledge.”
Frequently Asked Questions:
Are there any arrangements regarding COVID-19? Will the training go ahead as planned?

At the moment, we are planning for all of our training courses starting with September 2020 to go ahead in a physical location in Central London.

In case if circumstances change and we won’t be able to deliver the course in a classroom setting, we will deliver it virtually online via Zoom.

If this happens, we will get in touch and ask if you would like to go-ahead and attend the course virtually or if you prefer to cancel for a full refund.

What payment methods do you accept?

We accept all major credit and debit cards, and PayPal.

How can I get a 20% discount for my next training course?

You will receive this by email after completion of any of our classes.

What if I need to cancel my booking?

You can cancel your booking and receive a full refund up to one month in advance of the course start date.

If you made a booking for a seminar that starts in less than one month, you can cancel for a full refund within the 14 days of making the booking.

In case if we are unable to deliver a course in a physical classroom and had to move it online due to COVID-19, you can also cancel and request a full refund if you don’t want to attend the course virtually.

Are there any pre-requisites in order to attend this course?

A good understanding of financial markets and basics of Equity or FX derivatives is highly recommended for this course.

Want to run this training in-house?

Get in touch!

All our training courses can be tailored to your company needs and requirements.

Feel free to call us on +44 207 459 4445 or email and we’d be happy to help.

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