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所在平台: Coursera |
课程主页: https://www.coursera.org/learn/financial-engineering-computationalmethods
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课程名称：定价与模型校准的计算方法 概述：本课程专注于选项与利率产品的定价及模型校准中的计算方法。第一模块将介绍市场上不同类型的期权，并深入讨论有助于定价的数值技术，例如傅里叶变换（FT）和快速傅里叶变换（FFT）方法。课程将通过案例研究和Python代码，解释如Black-Merton-Scholes (BMS)、Heston、方差伽玛（VG）等模型，这些模型对理解股票价格演变至关重要。第二模块介绍如买卖价、隐含波动率和期权表面等概念，并演示如何使用暴力搜索、Nelder-Mead算法和BFGS算法优化例程进行市场期权价格的模型校准。第三模块引入利率及围绕这些工具构建的金融产品，并讲解远期利率、即期利率、掉期利率及利率期限结构的基本概念，进一步创建、校准及分析LIBOR和掉期曲线。通过Python代码演示债券、掉期及其他利率产品的定价。最后一模块重点介绍从业者在实际中使用的模型校准技术，用于估计利率过程并推导不同金融产品的价格。课程还将阐述几种用于利率模型校准的回归技术，最后介绍Vasicek模型和CIR模型在固定收益工具定价中的应用。 课程大纲： 1. 课程概述 2. 选项定价与数值方法：学习不同类型的期权，通过数值整合探讨期权定价的挑战与解决方案，包括傅里叶变换及FFT，并配以Python实例和案例分析。 3. 模型校准：介绍买卖价格及期权表面，学习如何选择模型及参数，应用优化算法（如暴力搜索、Nelder-Mead、BFGS）进行市场期权价格校准，及其在Python中的应用。 4. 利率及利率工具 I：从基本概念入手，如远期利率和即期利率，学习如何利用数据分析校准LIBOR与掉期曲线，通过Python代码定价债券和掉期。 5. 利率及利率工具 II：使用回归分析估计利率过程并校准模型，学习Vasicek模型和CIR模型在债券定价中的应用，通过练习加深理解。 此课程适合希望在金融工程和投资领域进一步发展的学员，通过实践与理论结合的方式，帮助学生掌握复杂金融工具的定价与分析技巧。
Name:Course Overview
Description:
Name:Option Pricing and Numerical Approach
Description: In this week, we will study option pricing via a numerical approach. In many cases, analytical (explicit) solution of option prices is not obtainable, which requires numerical solutions. For example, if we switch the stock dynamics from geometric Brownian motion to another model, or switch the option from vanilla style to exotic style, explicit pricing formula will become unrealistic. Firstly, we start from introduction to options, where you can learn different types of options and different perspectives of option market participants. Then we will talk about option pricing via numerical integration both in general and in details. In particular, we will focus on Fourier transform and fast Fourier transform (FFT). We also provide Python codes for you to learn how to apply these techniques in practice. In the end of this week, you will be exposed to several cases studies, from time cost comparison to different models. There are lots of models which estimates the stock price evolution. Among these models, we will mainly focus on Black-Merton-Scholes (BMS), Heston, and Variance Gamma (VG) model, where you will learn the motivation and characteristic of each model. Afterwards, you will have an assignment about option pricing, where you can utilize all the theoretical knowledge and Python codes to price different options under different stock dynamics.
Name:Model Calibration
Description:In this week, we will study model calibration, which follows the topics in last week. You have been exposed to many models, but you have no information about how to choose the model and parameters. Fortunately, you will learn how to solve this problem in this week from different approaches. Firstly, we start from an introduction to bid and ask prices and option surface. Then we will talk about the model calibration in regards with fitting the market option price, also with pictorial demonstration about implied volatility. Next, you will learn the calibration recipe, involving objective functions and initial parameter set. You will also learn how to do calibration in practice, which is an optimization problem. We will introduce three routines: brute-force search, Nelder-Mead algorithm, and BFGS algorithm. Except from learning these routines theoretically, you will also learn how to apply them in the optimization problem from Python codes. Followingly, you can apply what you learn about calibration in the assignment.
Name:Interest Rates and Interest Rate Instruments Part I
Description:We will start learning interest rates and interest rate instruments from this week. Interest rates play a very important role in measuring the future and present value of financial products. People also use market interest rates to analyze the economic situation. At the very beginning, we will introduce fundamental interest rate concepts, including forward rates, spot rates, swap rates and term structures of interest rates. Then we will apply data-driven analysis to calibrate LIBOR and swap curves and cross-correlations between these rates. Using the term structure of these interest rates, we should be able to price market value of bonds, swaps and other interest rate products. We also provide you with Python codes in order to show how to obtain the LIBOR curve and how to use it to price bonds. After learning this module, you will have a brief overview of interest rates and their applications in bond and swap pricing. We will talk about complex stochastic models and calibrate interest curves with these models next week.
Name:Interest Rates and Interest Rate Instruments Part II
Description:This week we will use different models to estimate interest rate processes and implement regression analysis to calibrate the processes. The models in this week are very important in practice. For instance, market makers need good models to help them interpolate or extrapolate market prices of illiquid interest-rate products, while speculators need models to help them understand the prices of fixed income securities so that they can bet on interest rates, etc. So in this module, we will first provide different regression techniques used to fit data in the market. Then we will introduce Vasicek model and CIR model for bond pricing. We also show how to use regression to fit data with our models. We provide all codes needed and also go through the codes to help you know how to apply them. At the end of the lecture, you will be asked to practice interest rate models by fitting LIBOR rates in the assignment.
This course focuses on computational methods in option and interest rate, product’s pricing and model calibration. The first module will introduce different types of options in the market, followed by an in-depth discussion into numerical techniques helpful in pricing them, e.g. Fourier Transform (FT) and Fast Fourier Transform (FFT) methods. We will explain models like Black-Merton-Scholes (BMS), Heston, Variance Gamma (VG), which are central to understanding stock price evolution, through case studies and Python codes. The second module introduces concepts like bid-ask prices, implied volatility, and option surfaces, followed by a demonstration of model calibration for fitting market option prices using optimization routines like brute-force search, Nelder-Mead algorithm, and BFGS algorithm. The third module introduces interest rates and the financial products built around these instruments. We will bring in fundamental concepts like forward rates, spot rates, swap rates, and the term structure of interest rates, extending it further for creating, calibrating, and analyzing LIBOR and swap curves. We will also demonstrate the pricing of bonds, swaps, and other interest rate products through Python codes. The final module focuses on real-world model calibration techniques used by practitioners to estimate interest rate processes and derive prices of different financial products. We will illustrate several regression techniques used for interest rate model calibration and end the module by covering the Vasicek and CIR model for pricing fixed income instruments.
