Quantitative Finance From First Principles

Yield curves, XVA, model calibration

What you'll learn

Learn how to bootstrap a yield curve from traded market instruments (deposits, forward rate agreements and swaps)

Learn how to value nominal bonds and interest rate swaps

Learn how to simulate short rates and yield curves using the Hull-White model

Learn how to bootstrap a survival probability from credit default swaps

Learn how to simulate exposure profiles for an interest rate swap through time

Learn how to calculate the credit/debit valuation adjustment for an interest rate swap

Learn how to value a swaption using the Black-76 model

Learn how to calibrate the Hull-White model with constant mean-reversion speed and piecewise constant volatility to swaptions

Requirements

Some mathematics and finance background will be beneficial, but not entirely necessary. The course focuses on practical implementation in Excel, which is a software that is relatively easy to pick up.

Description

The course, Quantitative Finance from First Principles, focuses on the practical implementation of topics that a quant uses in their day-to-day work.The course begins with an in-depth exploration of yield curve construction and bootstrapping techniques. Students will learn how to derive zero-coupon curves from market instruments. These yield curves form the foundation for pricing a wide range of fixed income and derivative instruments.The course then progresses to valuation adjustments (XVA), including Credit Valuation Adjustment (CVA) and Debit Valuation Adjustment (DVA). These are explored both conceptually and via numerical implementation, with an emphasis on Monte Carlo simulation.Model calibration is the final core theme, where students will learn to calibrate the Hull-White model to market data.Excel and Python are used to implement the models covered in the course, offering students hands-on experience with industry-standard tools. Excel is used for rapid prototyping, visualisation, and understanding the structure of financial calculations. Python, with its robust libraries such as NumPy and SciPy, has become an industry-standard tool. By working with both platforms, students develop a strong practical skill set that complements their theoretical knowledge and prepares them for real-world Quantitative Finance applications and model development.Become a well-respected Quantitative Analyst today!

Overview

Section 1: How to build a yield curve

Lecture 1 Interest rate basics

Lecture 2 Bond and swap market mechanics

Lecture 3 Bond and swap valuation

Lecture 4 Bond and swap curve construction

Section 2: How to model XVA

Lecture 5 Bootstrapping a survival probability curve

Lecture 6 The Hull-White model

Lecture 7 CVA and DVA

Section 3: How to calibrate the Hull-White model

Lecture 8 The Black-76 model and swaptions

Lecture 9 Mathematics behind the Hull-White model with piecewise constant volatility

Lecture 10 Pricing swaptions in the Hull-White model

Students looking to break into the field of quantitative finance,Auditors,Experienced professionals looking for a career change,Senior management wanting more detail regarding model methodology,Quantitative analysts,Actuaries