Excel与VBA在金融高级建模中的应用

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"Advanced Modeling in Finance Using Excel and VBA" 是一本专注于使用Excel和VBA进行高级金融建模的英文原版书籍，适合于财务、金融和IT交叉领域的专业人士学习使用。本书深入探讨了如何利用Excel的强大功能和VBA（Visual Basic for Applications）的编程能力来构建复杂的金融模型。在金融领域，建模是理解和分析风险、预测市场行为以及制定投资策略的关键工具。VBA作为Excel的内置脚本语言，能够自动化工作流程，提高效率，对于处理大量数据和实现定制化的金融模型尤其有用。书中可能涵盖了以下核心知识点： 1. **基础金融理论**：包括资本资产定价模型（CAPM）、有效市场假说（EMH）、现代投资组合理论（MPT）等，这些都是构建金融模型的基础。 2. **Excel应用**：如使用公式、函数（如PV, FV, IRR, NPV等）进行现金流分析，使用图表和数据分析工具进行可视化，以及使用数组公式和高级功能进行复杂计算。 3. **VBA编程**：讲解如何通过VBA编写宏，自定义函数，实现自动化操作，以及如何创建用户界面以交互式地操作模型。 4. **金融衍生品建模**：可能涉及期权定价模型，如布莱克-斯科尔斯模型（Black-Scholes Model），以及对期货、互换、信用违约掉期（CDS）等复杂产品的建模。 5. **风险管理**：介绍如何使用VaR（Value at Risk）模型来评估市场风险，以及使用敏感性分析和压力测试来分析模型的稳健性。 6. **利率和货币市场模型**：如无风险利率的期限结构建模，如Black-Derman-Toy模型或CIR模型，以及外汇市场的波动性和相关性分析。 7. **实操案例**：书中可能包含实际金融问题的案例研究，如公司财务分析、投资组合优化、项目融资等，帮助读者将理论知识应用于实践。 8. **最新金融市场技术**：可能会涵盖近年来出现的新金融产品和市场趋势，如金融科技（FinTech）在建模中的应用，以及大数据和机器学习在金融分析中的角色。通过阅读这本书，读者不仅可以提升在Excel和VBA方面的技能，还能深入理解金融建模的原理和实践，这对于在金融行业工作的专业人士来说，是提升专业能力的重要资源。

Introduction

We hope that our text, Advanced Modelling in Finance, is conclusive proof that a wide

range of models can now be successfully implemented using spreadsheets. The models

range across the complete spectrum of ﬁnance including equities, equity options and bond

options spanning developments from the early ﬁfties to the late nineties. The models are

implemented in Excel spreadsheets, complemented with functions written using the VBA

language within Excel. The resulting user-deﬁned functions provide a portable library of

programs with more than sufﬁcient speed and accuracy.

Advanced Modelling in Finance should be viewed as a complement (or dare we say,

an antidote) to traditional textbooks in the area. It contains relatively few derivations,

allowing us to cover a broader range of models and methods, with particular emphasis

on more recent advances.

The major theoretical developments in ﬁnance such as portfolio theory in the 1950s,

the capital asset pricing model in the 1960s and the Black–Scholes formula in the 1970s

brought with them analytic solutions that are now straightforward to calculate. The subse-

quent decades have seen a growing body of developments in numerical methods. With an

intelligent choice of parameters, binomial trees have assumed a central role in the more

numerically-intensive calculations now required to value equity and bond options. The

centre of gravity in ﬁnance now concerns the search for more efﬁcient ways of performing

such calculations rather than the theories from yesteryear.

The breadth of the coverage across ﬁnance and the sophistication needed for some

of the more advanced models are testament to the ability of Excel, the built-in functions

contained in Excel and the real programming environment that VBA provides. This allows

us to highlight the commonality of assumptions (lognormality), mathematical problems

(expectation) and numerical methods (binomial trees) throughout ﬁnance as a whole.

Without exception, we have tried to ensure a consistent and simple notation throughout

the book to reinforce this commonality and to improve clarity of exposition.

Our objective in writing a book that covers the broad range of subjects in ﬁnance

has proved to be both a challenge and an opportunity. The opportunity has provided

us with the chance to overview ﬁnance as a whole and, in so doing, to make impor-

tant connections and bring out commonalities in asset price assumptions, mathemat-

ical problems, numerical methods and Excel solutions. In the following sections we

summarise a few of these unifying insights that apply to equities, options and bonds

with regard to ﬁnance, mathematical topics, numerical methods and Excel features. This

is followed by a more detailed summary of the main topics covered in each chapter of

the book.

1.1 FINANCE INSIGHTS

The genesis of modern ﬁnance as a subject separate from economics started with

Markowitz’s development of portfolio theory in 1952. Markowitz used utility theory to

model the preferences of individual investors and to develop a mean–variance approach

2 Advanced Modelling in Finance

to examining the trade-off between return (as measured by an asset’s mean return) and

risk (measured by an asset’s variance of return). This subsequently led to the development

by Sharpe, Lintner and Treynor of the capital asset pricing model (CAPM), an equilibrium

model describing expected returns on equities. The CAPM introduced beta as a measure

of diversiﬁable risk, arguing that the creation of portfolios served to minimise the speciﬁc

risk element of total risk (variance).

The next great theoretical development was the equity option pricing formula of Black

and Scholes, which rested on the ability to create a (riskless) hedge portfolio. Contempora-

neously, Merton extended the Black–Scholes formula to allow for continuous dividends

and thus also options on commodities and currencies. The derivation of the original

formula required the solving of the diffusion (or heat) equation familiar from physics, but

was subsequently encompassed by the broader risk-neutral approach to the valuation of

derivatives.

1.2 ASSET PRICE ASSUMPTIONS

Although portfolio theory was derived through individual preferences, it could also have

been obtained by making assumptions about the distribution of asset price returns. The

standard assumption is that equity returns follow a lognormal distribution–equivalently we

can say that equity log returns follow a normal distribution. More recently, practitioners

have examined the effect of departures from strict normality (as measured by skewness

and kurtosis) and have also proposed different distributions (for example, the reciprocal

gamma distribution).

Although bonds have characteristics that are different from equities, the starting point

for bond option valuation is the short interest rate. This is frequently assumed to follow

the lognormal or normal distribution. The result is that familiar results grounded in these

probability distributions can be applied throughout ﬁnance.

1.3 MATHEMATICAL AND STATISTICAL PROBLEMS

Within the equities part, the mathematical problems concern optimisation. The optimi-

sation can also include additional constraints, exempliﬁed by Sharpe’s development of

returns-based style analysis. Beta is estimated as the slope coefﬁcient in a linear regression.

Options are valued in the risk-neutral framework as statistical expectations. The normal

distribution of log equity prices can be approximated by an equivalent discrete bino-

mial distribution. This binomial distribution provides the framework for calculating the

expected option value.

1.4 NUMERICAL METHODS

In the context of portfolio optimisation, the optimisation involves portfolio variance, and

the numerical method needed for optimisation is quadratic programming. Style analysis

also uses quadratic programming, the quantity to be minimised being the error variance.

Although not usually thought of as optimisation, linear regression chooses slope coef-

ﬁcients to minimise residual error. Here optimisation is of a different kind, regression

analysis, which provides analytical formulas to calculate the beta coefﬁcients.

Turning to option valuation, the binomial tree provides the structure within which

the risk-neutral expectation can be calculated. We highlight the importance of parameter

Introduction 3

choice by examining the convergence properties of three different binomial trees. Such

trees also allow the valuation of American options, where the option can be exercised at

any date prior to maturity.

With European options, techniques such as Monte Carlo simulation and numerical

integration are also used. Numerical search methods, in particular the Newton–Raphson

approach, ensure that volatilities implied by option prices in the market can be estimated.

1.5 EXCEL SOLUTIONS

The spreadsheets demonstrate how Excel can be used as a prototype for building models.

Within the individual spreadsheets, all the formulas in the cells can easily be examined

and we have endeavoured to incorporate all intermediate calculations in cells of their

own. The spreadsheets also allow the hallmark ability to ‘what-if’ by changing parameter

values in cells.

The implementation of all the models and methods occurs twice: once in the spread-

sheets and once in the VBA functions. This dual approach serves as an important check

on the accuracy of the numerical calculations.

Some of the VBA procedures are macros, normally seen by others as the main purpose

of VBA in Excel. However, the majority of the procedures we implement are user-deﬁned

functions. We demonstrate how easily these functions can be written in VBA and how

they can incorporate Excel functions, including the powerful matrix functions.

The Goal Seek and Solver commands within Excel are used in the optimisation tasks.

We show how these commands can be automated using VBA user-deﬁned functions and

macros. Another under-used aspect of Excel involves the application of array functions

(invoked by the CtrlCShiftCEnter keystroke combination) and we implement these in

user-deﬁned functions. To improve efﬁciency, our binomial trees in user-deﬁned functions

use one-dimensional arrays (vectors) rather than two-dimensional arrays (matrices).

1.6 TOPICS COVERED

There are four parts in the book, the ﬁrst part illustrating the advanced modelling features

in Excel followed by three parts with applications in ﬁnance. The three parts on applica-

tions cover equities, options on equities and options on bonds.

Chapter 2 emphasises the advanced Excel functions and techniques that we use in the

remainder of the book. We pay particular attention to the array functions within Excel

and provide a short section detailing the mathematics underlying matrix manipulation.

Chapter 3 introduces the VBA programming environment and illustrates a step-by-step

approach to the writing of VBA subroutines (macros). The examples chosen demonstrate

how macros can be used to automate and repeat tasks in Excel.

Chapter 4 moves on to VBA user-deﬁned functions, which have a crucial role

throughout the applications in ﬁnance. We emphasise how to deal with both scalar

and array variables–as input variables to VBA functions, their use in calculations and

ﬁnally as output variables. Again, we use a step-by-step approach for a number of

examples. In particular, we write user-deﬁned functions to value both European options

(the Black–Scholes formula) and American options (binomial trees).

Chapter 5 introduces the ﬁrst application part, that dealing with equities.

Chapter 6 covers portfolio optimisation, using both Solver and analytic solutions. As

will become the norm in the remaining chapters, Solver is used both in the spreadsheet

4 Advanced Modelling in Finance

and automated in a VBA macro. By using the array functions in Excel and VBA, we detail

how the points on the efﬁcient frontier can be generated. The development of portfolio

theory is divided into three generic problems, which recur in subsequent chapters.

Chapter 7 looks at (equity) asset pricing, starting with the single-index model and

the capital asset pricing model (CAPM) and concluding with Value-at-Risk (VaR). This

introduces the assumption that asset log returns follow a normal distribution, another

recurrent theme.

Chapter 8 covers performance measurement, again ranging from single-parameter

measures used in the very earliest days to multi-index models (such as style analysis) that

represent current best practice. We show, for the ﬁrst time in a textbook, how conﬁdence

intervals can be determined for the asset weights from style analysis.

Chapter 9 introduces the second application part, that dealing with options on equities.

Building on the normal distribution assumed for equity log returns, we detail the creation

of the hedge portfolio that is the key insight behind the Black–Scholes option valuation

formula. The subsequent interpretation of the option value as the discounted expected

value of the option payoff in a risk-neutral world is also introduced.

Chapter 10 looks at binomial trees, which can be viewed as a discrete approxima-

tion to the continuous normal distribution assumed for log equity prices. In practice,

binomial trees form the backbone of numerical methods for option valuation since they

can cope with early exercise and hence the valuation of American options. We illustrate

three different parameter choices for binomial trees, including the little-known Leisen and

Reimer tree that has vastly superior convergence and accuracy properties compared to the

standard parameter choices. We use a nine-step tree in our spreadsheet examples, but the

user-deﬁned functions can cope with any number of steps.

Chapter 11 returns to the Black–Scholes formula and shows both its adaptability

(allowing options on assets such as currencies and commodities to be valued) and its

dependence on the asset price assumptions.

Chapter 12 covers two alternative ways of calculating the statistical expectation that

lies behind the Black–Scholes formula for European options. These are Monte Carlo

simulation and numerical integration. Although these perform less well for the simple

options we consider, each of these methods has a valuable role in the valuation of more

complicated options.

Chapter 13 moves away from the assumption of strict normality of asset log returns and

shows how such deviation (typically through differing skewness and kurtosis parameters)

leads to the so-called volatility smile seen in the market prices of options. Efﬁcient

methods for ﬁnding the implied volatility inherent in European option prices are described.

Chapter 14 introduces the third application part, that dealing with options on bonds.

While bond prices have characteristics that are different from equity prices, there is a

lot of commonality in the mathematical problems and numerical methods used to value

options. We deﬁne the term structure based on a series of zero-coupon bond prices, and

show how the short-term interest rate can be modelled in a binomial tree as a means of

valuing zero-coupon bond cash ﬂows.

Chapter 15 covers two models for interest rates, those of Vasicek and Cox, and Ingersoll

and Ross. We detail analytic solutions for zero-coupon bond prices and options on zero-

coupon bonds together with an iterative approach to the valuation of options on coupon

bonds.

Chapter 16 shows how the short rate can be modelled in a binomial tree in order

to match a given term structure of zero-coupon bond prices. We build the popular

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