Course description
Fundamentals of Quantitative Finance
Explore the details behind financial modeling and derivatives pricing
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.
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Upcoming start dates
Choose between 2 start dates
Suitability - Who should attend?
- 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.
Outcome / Qualification etc.
What will you learn?
By the end of the course, you will:
- Gain a solid understanding of the Black-Scholes framework and its applications within the financial markets.
- Refresh your knowledge on statistics, probability theory and Partial Differential Equations (PDEs).
- Be able to construct a simple Brownian motion process and become familiar with random process modeling.
- Appreciate the notions of complete and arbitrage-free markets and what they mean for asset valuation.
- Explore how Finite Difference and Monte Carlo methods are used to value complex financial derivatives.
- Understand the relationship between the Binomial model and the Black-Scholes formula.
- Be able to derive various risk metric formulas for European vanilla options.
- Understand and apply different approaches to volatility modeling and forecasting.
- Know how to back out risk-neutral probabilities from listed option prices and construct a probability distribution.
- Learn how to amend the Black-Scholes framework to new products and payoffs.
- And much more!
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.
Training Course Content
Day 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.
- Review of Financial Derivatives:
- Futures and forward contracts.
- Options.
- Barrier options.
- Binary and digital options.
- Asian options.
- Structured products.
- 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:
- 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.
- 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:
- 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.
- 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.
- 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:
- Fundamental Theorem of Asset Pricing:
- Arbitrage and arbitrage-free markets.
- Complete markets.
- Equivalent martingale measure.
- Market price of risk.
- 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.
- 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:
- Calibration of Derivatives Pricing Models:
- What is calibration?
- Black-Scholes formula and implied volatility.
- Risk-neutral probabilities.
- Breeden-Litzenberger formula.
- Local volatility.
- 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.
- 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.
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