Control Finance ACC 2010

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Control Systems Methods in Finance:Modeling and Optimal Trading

James A. PrimbsManagement Science and Engineering

Stanford University

ACC 2010

Baltimore, MD

June 30, 2010


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Introduction

Outline

Future Outlook

Modeling Market Dynamics

Optimal Trading in Financial Market


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Important Early Developments in Quantitative Finance

1964: William Sharpe publishes the Capital Asset Pricing Model. (Lintner,

Mossin, and Treynor independently discover the same theory).

1955: Harry Markowitz develops mean-variance portfolio optimization in a

single period framework in his PhD thesis from University of Chicago.Quantitative finance is born.

1969+: Samuelson (69) and especially Merton (69,71,73) publish dynamic

portfolio optimization work using control theory and dynamic programming.

1973: Black and Scholes (with input from Merton) publish the seminal paper

on option pricing theory that shows that dynamic strategies can be used to

create options. Option pricing theory takes off and quantitative finance is

here to stay.
http://en.wikipedia.org/wiki/File:Robert_C._Merton.jpghttp://www.bing.com/reference/search?q=paul%20samuelson&FORM=K1RE1http://upload.wikimedia.org/wikipedia/en/5/5a/Markowitz_1.jpghttp://en.wikipedia.org/wiki/File:William_sharpe_2007.jpg


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Introduction

Outline

Future Outlook


Optimal Trading in Financial Markets


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Control Problems in Finance

What can we control?

We control what we hold inour portfolio and this

determines our wealth

dynamics.

Most of the standard financial engineering problems can

be cast in a stochastic optimal control framework.

)( rSdtdSurWdtdW

How many shares do you want?

SdZSdtdS

rBdtdB

Example:


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)( rSdtdSurWdtdW

SdZSdtdS

rBdtdB

Example:

Stochastic

System

Dynamics

Things can quickly get more complicated:

Transaction CostsMargin Constraints

Liquidity Constraints

Market Impact


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What is the objective?

Portfolio Optimization: Maximize the utility of wealth.

))](([max TWUEu

Who uses this: Assets Management Firms, Hedge Funds, Investment

Advisors. All of us! (Think about your retirement account!)



1. Grow Wealth


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Dynamic Hedging: Minimize the difference between wealth and a

payoff at a specified time T.

2))((min payoffTWE

u

Who uses this: Investment Banks (Option Pricing, Risk Management),

Hedge Funds (Statistical Arbitrage).



2. Replicate a payoff


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Index Tracking: Minimize the tracking error between your wealth and

a pre-specified index such as the S&P 500.

0

2))()((min dttItWeE

t

u

Who uses this: Asset Management Firms (variations such as beat a

benchmark index), ETFs.



3. Track an index


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What are the challenges and

opportunities for control engineers?

Bottom line: Do what we already do, just tailor it to

financial engineering applications.

Create practical, engineering oriented solutions to real

financial engineering problems.

Handle transaction costs and constraints

Efficient algorithms for large problems sizes.

Examples:


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Introduction

Outline

Future Outlook




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Financial Market Dynamics

Price dynamics results from the interaction of manytraders using a variety of strategies and objectives.

Lots offeedback loops! To understand such a system, one

must understand feedback. That is what we know best

Market

Financial

Institutions

Funds

Individuals

Government

Regulation


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Motivating Example 187 Stock Market Crash

-0.25

-0.2

-0.15

-0.1

-0.05

0

0.05

0.1

0.15

1

1/19/1987

12/1/1987

1

2/10/1987

1

2/21/1987

Returns

Returns

0

500

1000

1500

2000

2500

3000

8/27/1987

9/4/1987

10/1/1987

10/9/1987

11/12/1987

11/20/1987

12/17/1987

12/28/1987

Stock Prices

DJI

The Dow Jones Industrial Average Drops over 500 points (more than 22%) in

a single day!

There is no apparent fundamental reason for the crash. What happened?

The finger is pointed at feedback effects from so called portfolio insurance

ideas. (See the Brady Commission Presidential Report.)

Crash!


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Motivating Example 2Stock Pinning

Stocks on options with high open interest can become pinned to the strike

price at expiration. Why does this happen?One explanation: Feedback effects from Black-Scholes option pricing theory

based dynamic hedging strategies are responsible.

See Avellaneda and Lipkin (03), Primbs and Rathinam (09).

Strike PriceStock Path


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Motivating Example 3August 2007 Hedge Fund Unwinding

See What Happened to the Quants in August 2007? by Khandani and Lo (07).

The price impact of the unwind causes other hedge funds to de-leverage

which exacerbates losses.

Top quant hedge funds lose big: Renaissance loses 8.7% in first 10 days of

August. Highbridge drops 18%. Tykhe is down 20%.

Note: Nothing unusual in overall market during that time. Losses were narrowly

confined to model driven long/short market neutral strategies. Could a control

systems/feedbacks analysis explain and even have predicted this?

What happened: The rapid unwinding of one or more quantitative market

neutral portfolios ripples through the entire quant hedge fund industry.

Long Short


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Feedback Phenomena

Lots of interesting feedback phenomena occurring in the

market!

Control and systems perspective can help to understand,

explain, and perhaps even predict and mitigate

phenomena.

1. Volatility Clustering

2. Heavy Tail Distributions

3. Volatility Smile and Smirks

4. 1000 point drop in 2010.

5. Etc

Theres more!


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Introduction

Outline

Future Outlook




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Looking to the Future

Control and systems engineering can become a major tool

for the design, optimal management, and understanding of

financial systems.

Lots of interesting problems that have not been explored

from the control perspective.

We have the tools to address real problems whose impact

is felt on a global scale. An exciting opportunity!

Control Finance ACC 2010

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