# Applied Probabilistic Calculus for Financial Engineering

An Introduction Using R

Wiley (Verlag)
• erschienen am 11. September 2017
• |
• 536 Seiten

 E-Book | ePUB mit Adobe DRM | Systemvoraussetzungen
978-1-119-38804-3 (ISBN)

Illustrates how R may be used successfully to solve problems in quantitative finance
Applied Probabilistic Calculus for Financial Engineering: An Introduction Using R provides R recipes for asset allocation and portfolio optimization problems. It begins by introducing all the necessary probabilistic and statistical foundations, before moving on to topics related to asset allocation and portfolio optimization with R codes illustrated for various examples. This clear and concise book covers financial engineering, using R in data analysis, and univariate, bivariate, and multivariate data analysis. It examines probabilistic calculus for modeling financial engineering--walking the reader through building an effective financial model from the Geometric Brownian Motion (GBM) Model via probabilistic calculus, while also covering Ito Calculus. Classical mathematical models in financial engineering and modern portfolio theory are discussed--along with the Two Mutual Fund Theorem and The Sharpe Ratio. The book also looks at R as a calculator and using R in data analysis in financial engineering. Additionally, it covers asset allocation using R, financial risk modeling and portfolio optimization using R, global and local optimal values, locating functional maxima and minima, and portfolio optimization by performance analytics in CRAN.
* Covers optimization methodologies in probabilistic calculus for financial engineering
* Answers the question: What does a "Random Walk" Financial Theory look like?
* Covers the GBM Model and the Random Walk Model
* Examines modern theories of portfolio optimization, including The Markowitz Model of Modern Portfolio Theory (MPT), The Black-Litterman Model, and The Black-Scholes Option Pricing Model
Applied Probabilistic Calculus for Financial Engineering: An Introduction Using R s an ideal reference for professionals and students in economics, econometrics, and finance, as well as for financial investment quants and financial engineers.
 Reihe: Auflage: 1. Auflage Sprache: Englisch Verlagsort: Newark | USA Verlagsgruppe: John Wiley & Sons Dateigröße: 7,95 MB Schlagworte: ISBN-13: 978-1-119-38804-3 (9781119388043) ISBN-10: 111938804X (111938804X)
weitere Ausgaben werden ermittelt
BERTRAM K. C. CHAN, PhD, is Consulting Biostatistician at the Loma Linda University Health, School of Medicine, Loma Linda, CA. Dr. Chan is also Software Development and Forum Lecturer at the School of Public Health, LLUH Department of Biostatistics and Epidemiology.
Preface
Dedication
Chapter 1: Introduction to Financial Engineering
1 Introduction to Financial Engineering
1.1 What is Financial Engineering?
1.2 The Meaning of the Title of this Book
1.3 The Continuing Challenge in Financial Engineering
1.4 "Financial Engineering 101": Modern Portfolio Theory[2]
1.5 Asset Class Assumptions Modeling
1.6 Typical Examples of Proprietary Investment Funds
1.7 The Dow Jones Industrial Average (DJIA) and Inflation
1.8 Some Less Commendable Stock Investment Approaches
1.9 Developing Tools for Financial Engineering Analysis Solutions to Exercises in Chapter 1:
Chapter 2: Probabilistic Calculus for Modeling Financial Engineering
2.1 Introduction to Financial Engineering
2.2 Mathematical Modeling in Financial Engineering
2.3 Building an Effective Financial Model from GBM via Probabilistic Calculus
2.4 A Continuous Financial Model Using Probabilistic Calculus (Stochastic Calculus, Ito Calculus)
2.5 Numerical Examples of Representation of Financial Data Using R
Chapter 3: Classical Mathematical Models in Financial Engineering and Modern Portfolio Theory
3.0 An Introduction to the Cost of Money in the Financial Market
3.1 Modern Theories of Portfolio Optimization
3.2 The Black-Litterman Model
3.3 The Black-Scholes Option Pricing Model
Chapter 4: Data Analysis Using R Programming
4.1 Data and Processing
4.2 Beginning R
4.3 R as a Calculator
4.4 Using R in Data Analysis in Financial Engineering
4.5 Univariate, Bivariate, and Multivariate Data Analysis
Appendix 1: Documentation for the plot function
Special References for Chapter 4
Chapter 5: Assets Allocation Using R
5.1 Risk Aversion and the Assets Allocation Process
5.2 Classical Assets Allocation Approaches
5.3 Allocation with Time Varying Risk Aversion
5.4 Variable Risk Preference Bias
5.5 A Unified Approach for Time Varying Risk Aversion
5.6 Assets Allocation Worked Examples
Chapter 6: Financial Risk Modeling and Portfolio Optimization Using R
6.1 Introduction to the Optimization Process
6.2 Optimization Methodologies in Probabilistic Calculus for Financial Engineering
6.3 Financial Risk Modeling and Portfolio Optimization
References
Index

# 1Introduction to Financial Engineering

## 1.1 What Is Financial Engineering?

In today's understanding and everyday usage, financial engineering is a multidisciplinary field in finance, and in theoretical and practical economics involving financial theory, the tools of applied mathematics and statistics, the methodologies of engineering, and the practice of computer programming. It also involves the application of technical methods, especially in mathematical and computational finance in the practice of financial investment and management.

However, despite its name, financial engineering does not belong to any of the traditional engineering fields even though many financial engineers may have engineering backgrounds. Some universities offer a postgraduate degree in the field of financial engineering requiring applicants to have a background in engineering. In the United States, ABET (the Accreditation Board for Engineering and Technology) does not accredit financial engineering degrees. In the United States, financial engineering programs are accredited by the International Association of Quantitative Finance.

Financial engineering uses tools from economics, mathematics, statistics, and computer science. Broadly speaking, one who uses technical tools in finance may be called a financial engineer: for example, a statistician in a bank or a computer programmer in a government economic bureau. However, most practitioners restrict this term to someone educated in the full range of tools of modern finance and whose work is informed by financial theory. It may be restricted to cover only those originating new financial products and strategies. Financial engineering plays a critical role in the customer-driven derivatives business that includes quantitative modeling and programming, trading, and risk managing derivative products in compliance with applicable legal regulations.

A broader term that covers anyone using mathematics for practical financial investment purposes is "Quant", which includes financial engineers.

## 1.2 The Meaning of the Title of This Book

The wide use of the open-source computer software R testifies to its versatility and its concomitant increasing popularity, bearing in mind that the ubiquitous application of R is most probably due to its suitability for personal mobile-friendly desktop/laptop/panel/tablet/device computer usage. The Venn diagram that follows illustrates the interactional relationship in this context.Three subjects enunciated in this book are as follows:

1. Applied probabilistic calculus (APC)
2. Assets allocation and portfolio optimization in financial engineering (AAPOFE)
3. The computer language (R)

The concomitant relationship may be graphically illustrated by the mutually intersecting relationships in the following Venn diagram, APC n AAPOFE n R.

Thus, this book is concerned with the distinctive subjects of importance and relevance within these areas of interest, including Applied Probabilistic Calculus and Assets Allocation and Portfolio Optimization in Financial Engineering, namely, APC n FE, to be followed by critical areas of the computational and numerical aspects of Applied Probabilistic Calculus for (Assets Allocation and Portfolio Optimization in) Financial Engineering: An Introduction Using R, namely, APC n FE n R. This is represented by the "red" area in Figure 1.1, being the common area of mutual intersection of the three areas of special interest.

Figure 1.1 Applied Probabilistic Calculus for Financial Engineering: An Introduction Using R namely, APC n FE n R.

## 1.3 The Continuing Challenge in Financial Engineering

In the case of the investment of Mr. and Mrs. Smith (as introduced in the Preface of this book), financial engineering by the investment management company XYZ established a portfolio consisting of four accounts:

Account 1: A Family Trust

1. \$648,857.13 (change for the day: +\$150.75, +0.02%) 30.73% of Portfolio

Account 2: Individuals Trust

1. \$504,669.30 (change for the day: +3,710.04, +0.74%)

Account 3: Traditional IRA for Person A

1. \$476,096.53 (change for the day: \$2,002.22, +0.42%)

Account 4: Traditional IRA for Person B

1. \$457,502.17 (change for the day: \$142.00, +0.03%)

The positions of these accounts are as follows:

Account 1: A. Cash and cash equivalents \$626,331.02 (97.58%) B. Equities and options \$15,839.25 (2.42%) Account 2: A. Common stock - equities and options (22.71%) B. Money market - cash and cash equivalents (55.22%) C. Mutual fund, ETFs, and closed-end funds (22.07%) Account 3: A. Cash and cash equivalent \$247,467.33 (52.2%) B. Equities and options (3.42%) C. Money market sweeps \$247,467.33 (44.38%) Deposit cash account \$247,447.91, account dividend 19.42 Account 4: A. Cash and cash equivalents (93.65%) B. Mutual funds, ETPs, and closed-end funds (44.38%)

At 11:30 p.m., Tuesday, November 15, 2016: the Smiths' account balance = \$2,100,661.36 9

### 1.3.1 The Volatility of the Financial Market

The dynamics and volatility of the financial market is well known.

For example, consider the Chicago Board of Options Exchange (CBOE) index:

CBOE Volatility Index®: Chicago Board Options Exchange index (symbol: VIX®) is the index that shows the market's expectation of 30-day volatility. It is constructed using the implied volatilities of a wide range of S&P 500 index options. This volatility is meant to be forward looking, is calculated from both calls and puts, and is a widely used measure of market risk, often referred to as the "investor fear gauge."

The VIX volatility methodology is the property of CBOE, which is not affiliated with Janus.

Clearly, Figure 1.2 reflects the dynamic nature of a typical stock market over the past 20 years. One wonders if a rational financial engineering approach may be developed to sustain the two objectives at hand simultaneously:

1. To maintain a steady level of investment
2. To produce a steady income for the investors

Figure 1.2 Chicago Board of Options Exchange (CBOE) Volatility Index.

The remainder of this book will provide rational approaches to achieve these joint goals.

### 1.3.2 Ongoing Results of the XYZ-LPL Investment of the Account of Mr. and Mrs. Smith

Let us first examine the results of this investment opportunity, as seen over the past 10 years approximately.

Investment Results of the XYZ-LPL (Linsco (1968) and Private Ledger (1973)) is illustrated as follows:

LPL Financial Holdings (commonly referred to as LPL Financial) is the largest independent broker-dealer in the United States. The company has more than 14,000 financial advisors, over \$500 billion in advisory and brokerage assets, and generated approximately \$4.3 billion in annual revenue for the 2015 fiscal year. LPL Financial was formed in 1989 through the merger of two brokerage firms - Linsco (established in 1968) and Private Ledger (established in 1973) - and has since expanded its number of independent financial advisors both organically and through acquisitions. LPL Financial has main offices in Boston, Charlotte, and San Diego. Approximately 3500 employees support financial institutions, advisors, and technology, custody, and clearing service subscribers with enabling technology, comprehensive clearing and compliance services, practice management programs and training, and independent research.

LPL Financial advisors help clients with a number of financial services, including equities, bonds, mutual funds, annuities, insurance, and fee-based programs. LPL Financial does not develop its own investment products, enabling the firm's investment professionals to offer financial advice free from broker/dealer-inspired conflicts of interest.

1. Revenue: US\$4.37 billion (2014)
2. Headquarters: 75 State Street, Boston, MA, USA
3. Traded as: NASDAQ: LPLA (https://en.wikipedia.org/wiki/LPL_Financial)

Over the past 10 years, the Smiths' received, on a monthly basis, a net income of \$10,947.03. Thus, annually, the income has been

And, the total income for the past 10 years has been

Illustrated hereunder in Figure 1.3 is a snapshot of one of the four investment accounts of the Smiths'. Note the following...

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