Interest Rate Models

所在平台: Coursera

课程主页: https://www.coursera.org/learn/interest-rate-models

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课程简介

课程名称：利率模型 课程概述：本课程为您提供了一个关于利率及相关合同的简单介绍。内容包括LIBOR、债券、远期利率协议、互换、利率期货、上限、下限和互换选项等。我们将学习如何应用持续期和凸度这两个基本工具来管理债券投资组合的利率风险，并获得使用市场数据估计期限结构的实践。我们还将学习随机微积分中的基本知识，以帮助您设计多种随机利率模型。同时，我们将复习套利定价理论，为金融衍生品定价奠定基础。本课程还将涵盖行业标准的布莱克（Black）和巴赫列（Bachelier）公式，用于定价上限、下限和互换选项。课程结束时，您将掌握如何将利率模型与市场数据进行校准以及如何定价利率衍生品。 课程大纲： 1. **简介** 2. **利率及相关合同** 学习利率的不同概念及其相关合同，包括贷款的利息和债券的定义，LIBOR的作用以及利率互换的基本机制。同时介绍持续期和凸度作为管理债券投资组合利率风险的工具。 3. **期限结构的估计** 学习如何从市场数据中估计期限结构，涵盖精确方法和光滑方法的比较，以及主成分分析在期限结构中的应用。 4. **随机模型** 基于随机微积分的利率期限结构演变模型快速入门，涉及布朗运动、随机积分和随机过程，为设计多种随机利率模型提供工具，同时复习套利定价理论，应用于债券期权定价。 5. **利率衍生品** 应用所学知识定价利率衍生品，聚焦于利率期货、上限、下限和互换选项的标准衍生品，推导行业标准的布莱克和巴赫列公式，并通过案例研究学习如何将随机利率模型校准到市场数据。 6. **期末测验** 评估学习成果。 通过本课程，您将建立起对利率模型及衍生品定价的系统理解，具备分析和管理利率风险的能力。

课程大纲

Name:Introduction

Description:

Name:Interest Rates and Related Contracts

Description:We learn various notions of interest rates and some related contracts. Interest is the rent paid on a loan. A bond is the securitized form of a loan. There exist coupon paying bonds and zero-coupon bonds. The latter are also called discount bonds. Interest rates and bond prices depend on their maturity. The term structure is the function that maps the maturity to the corresponding interest rate or bond price. An important reference rate for many interest rate contracts is the LIBOR (London Interbank Offered Rate). Loans can be borrowed over future time intervals at rates that are agreed upon today. These rates are called forward or futures rates, depending on the type of the agreement. In an interest rate swap, counterparties exchange a stream of fixed-rate payments for a stream of floating-rate payments typically indexed to LIBOR. Duration and convexity are the basic tools for managing the interest rate risk inherent in a bond portfolio. We also review some of the most common market conventions that come along with interest rate market data.

Name:Estimating the Term Structure

Description:We learn how to estimate the term structure from market data. There are two types of methods. Exact methods produce term structures that exactly match the market data. This comes at the cost of somewhat irregular shapes. Smooth methods penalize irregular shapes and trade off exactness of fit versus regularity of the term structure. We will also see what principal component analysis tells us about the basic shapes of the term structure.

Name:Stochastic Models

Description:Models for the evolution of the term structure of interest rates build on stochastic calculus. We start with a crash course in stochastic calculus, which introduces Brownian motion, stochastic integration, and stochastic processes without going into mathematical details. This provides the necessary tools to engineer a large variety of stochastic interest rate models. We then study some of the most prevalent so-called short rate models and Heath-Jarrow-Morton models. We also review the arbitrage pricing theorem from finance that provides the foundation for pricing financial derivatives. As an application we price options on bonds.

Name:Interest Rate Derivatives

Description:We apply what we learnt to price interest rate derivatives. Specifically, we focus on the standard derivatives: interest rate futures, caps and floors, and swaptions. We derive the industry standard Black and Bachelier formulas for cap, floor, and swaption prices. In a case study we learn how to calibrate a stochastic interest rate model to market data.

Name:Final Quiz

Description:

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