OIS Discounting - Curve Bootstrapping - Part 1: The Theory

🎬 In this video, learn the theory behind the construction of an OIS Discounting Curve using the bootstrapping methodology

Have you ever wondered about how yield curves and discount factor curves are constructed from quoted instruments? Have you always wondered what bootstrapping really meant? This video will show you just that: from the very general concepts to the detailed mathematical formulas and the numerical tools (e.g. interpolation & root-finding algorithms) necessary to build such curves.

Along with the theory, we will include a complete and self-contained example in an Excel spreadsheet, replicating exactly what is happening in the C++ code of ORE.
Please note this spreadsheet should be made available in the coming weeks as part of a new repository completely dedicated to ORE-Related Tools - Please subscribe to get notifications.

The underlying instrument driving all these calculations is an equity option which data can already be found in ORE repository: https://github.com/OpenSourceRisk/Eng...

The spreadsheet used as support in the second part of the video can be found in the ORE Tools repository:
https://github.com/OpenSourceRisk/Too...

We will split the video into 2 videos: this video is about the theory
Chapter 1 - We will first present the general principles of bootstrapping, what it is, why it’s so important, the different types, the choice of instruments…
Chapter 2 - Then we demonstrate some of the mathematical formulas used for OIS curve bootstrapping

Then the second video will be the practice part:
Chapter 3 - We will show you an example in Excel which is actually a complete parallel implementation of the bootstrapping calculations happening in ORE.
It means that everything which is presented in the Excel spreadsheet will have a corresponding implementation in C++, with the exact same data and the exact same results

The spreadsheet can be found on our Tools repository:
https://github.com/OpenSourceRisk/Too...

Reference: TA004
Category: Trades & Analytics
Complexity: Beginner
Operating System: Windows

Link(s) to Supporting Document(s):
ORE Repository: https://github.com/OpenSourceRisk
ORE Website: https://www.opensourcerisk.org/

Author(s): Alexis David
Speaker(s): Alexis David
Editor(s): Alexis David

Prerequisite(s):
TA001 - Equity Option with Implied Volatility Surface:    • How to price an Equity Option with Implied...  
FC003 - How to Change the Reporting Currency:    • How to Change the Collateralization Curren...  

Chapters & Key Moments of the video:

00:00 - Introduction
Chapter 1 - General Principles
02:08 - 1.a. Swap vs Bond Market
04:22 - 1.b. OIS Introduction
07:10 - 1.c. Bootstrapping High-Level Principles
Chapter 2 - Bootstrapping Theory
09:37 - 2.a. Interest Rate Types
12:00 - 2.b. Schedule Definition
17:18 - 2.c. Instrument Definition - Deposit Explanation
19:23 - 2.c. Instrument Definition - General Fixed-Floating Swap
21:49 - 2.c. Instrument Definition - OIS Floating Rate Introduction
24:42 - 2.c. Instrument Definition - Current Bootstrapping Case (first part)
26:27 - 2.c. Instrument Definition - OIS Explanation
28:53 - 2.c. Instrument Definition - Current Bootstrapping Case (second part)
29:52 - 2.c. Instrument Definition - Cashflow Schedule Examples
32:26 - 2.d. Boostrapping Explanation - OIS Floating Rate - Calculations Summary (first part)
33:09 - 2.d. Boostrapping Explanation - OIS Compounding Rate - Alternative Equations
36:40 - 2.d. Boostrapping Explanation - OIS Floating Rate - Calculations Summary (second part)
37:05 - 2.d. Boostrapping Explanation - OIS Floating Leg Calculation
38:00 - 2.d. Boostrapping Explanation - Analytical Case
39:18 - 2.d. Boostrapping Explanation - Root-Finding Case (first part)
42:36 - 2.d. Boostrapping Explanation - Log-Linear Interpolation
45:19 - 2.d. Boostrapping Explanation - Root-Finding Case (second part)
46:51 - 2.d. Boostrapping Explanation - Z-Spread Curve
47:57 - 2.d. Boostrapping Explanation - Next Steps Example
49:03 - Outro

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