Week 4 and 5: Utility functions
1. Profit maximization of a non financial corporate
2. Consumer problem
3. Pricing a Bond
4. Pricing of an Option (Risk Neutral transformation)
5. Equilibrium and animal spirits
6. Implied preferences
7. Certainty Equivalen
Basic Instruments
4/17/17
Charles S. Tapiero, FRE/NYU-SE
1
Financial Instruments and Risk
Management
There are many financial instruments currently being used by corporate officers
and in financial markets. In fact, the number of such instrument is a true
Risk Exposure
Measurement
Content
VaR .and expected shortfall
Regret
VaR
VaR or Quantile Risk Exposure
Value at Risk is a practical measure of risk exposure that has become an
important tool for financial risk managers. It is a quantile measure
seeking to
Option Pricing Theory
1
Sebastien Galy, NYU Polytech
4/17/17
This class
1. Concept of filtration
2. Concept of completeness starting from reality
down to the models.
3. Discrete time pricing
Group projects on which you will be graded.
2
4/17/17
Incomp
Measuring Volatility
Volatility: Captures much but not
all
Volatility combined with fear defined your expected returns over
the risk free rate in a simple and highly stable world where
movements are defined by only the mean and variance
VAR(X)=E(X-E(X)2=E
Week 5: Midterm review
Sebastien Galy, NYU Poly Tech Institute
4/17/17
Knightian uncertainty or the unknown unknown e.g. conquistador
landing in South America
Incomplete Markets
Equilibrium with inelastic supply and demand for risk
utility theory
Prospe
Risk Measurement
Lecture 2
Defining measures
Measure and examples of report
Example of risks
Portfolio management risks
Distributions
Defining Measures
Concept of measure
Measurements define what we know
and want we do not know or are not
accounting for -
Agent view of the economy
1
Sebastien Galy, NYU Poly Tech Institute
4/17/17
Agents
Firm
Consumer
Reserve Manager
Asset Manager
Insurer
Charles S. Tapiero FRE-SE
2
1. firms problem: non financial corporate
3
Sebastien Galy, NYU Poly Tech Institute
4/17/17
Financial Risk Management
and Asset Pricing
Sebastien Galy
1
Course Outline: Motivation
Assets Pricing and Risk management are both fundamental
foundations to Financial and Risk Engineering.
They require an appreciation of financial economic theories,
mat
Defining Risk and
Uncertainty
and an introduction to Risk Management
4/17/17
Charles S. Tapiero, FRE/NYU-SE
1
Plan
Risk is a Big Business
Defining Risk vs Uncertainty
Risk Management
Example with credit risk
Dual reality: Risk as seen from risk taker vs r
International Series in Operations
Research & Management Science
Volume 188
Series Editor:
Frederick S. Hillier
Stanford University, CA, USA
Special Editorial Consultant:
Camille C. Price
Stephen F. Austin State University, TX, USA
For further volumes:
ht
Financial Risk Management
and Asset Pricing
Week 11: Utility and CAPM
Risk preferences
Utility
Risk taking: Would you pay $2 for a one in a million chance to
win $1,000,000?
Risk aversion: Would you pay $2 to avoid a one in a million
chance to lose $1
Financial Risk Management and
Asset Pricing
Week 5: Derivatives
Derivatives
Are derivatives evil?
Must they be regulated?
Did a formula bring down Wall Street?
What would you do if you were:
A trader?
An investor?
A regulator?
A legislator?
Dinner Der
Financial Risk Management and
Asset Pricing
Week 1
Philip Maymin, [email protected]
Any Questions?
NYU Classes
Intermission
Financial Risk Management and Asset Pricing:
What are we talking about?
What is finance?
What is risk?
What does it mean to manag
Any Regulation of Risk Increases Risk
Presentation by Philip Maymin
Joint work with Zak Maymin
Any Regulation of Risk Increases Risk
(not legislation)
Approaches:
Mathematical
Empirical
Experimental
Algorithmic
(systemic risk)
Regulation vs. Legislation
W
FRE6123: Financial Risk
Management and Asset Pricing
Week 2: Volatility
Homework
Bastiats Broken Window Fallacy
That Which is Seen, and That Which is Not Seen
Frederic Bastiat, 1850
The default that is not seen
There are two states for the risky bond: it
Financial Risk Management
and Asset Pricing
Week 10: Intro to Arrow-Debreu and Utility
Binomial Option Pricing
European
American
When should American calls be
exercised early?
1. Never
2. Possibly the day before the ex date of a large dividend,
but usua
Financial Risk Management
and Asset Pricing
Week 12: Alternative Portfolio
Construction, and Market Efficiency
Alternative Portfolio Construction
Mean-variance efficient frontier:
Weights of tangency portfolio
Black-Litterman:
Blend of MVE and Bayes
Financial Risk Management and
Asset Pricing
Week 8: Derivatives Continued
Option Types
Call
Payoff at maturity: Max[S K, 0]
Put
Payoff at maturity: Max[K S, 0]
When can you exercise?
European: at maturity
American: at any time
Intrinsic value
If
Financial Risk Management
and Asset Pricing
Week 9: Derivatives Concluded
Binomial Option Pricing Model
Say a stock is now at $100 and either goes up to $120 or
down to $90. A bond costs $90 now and will cost $100 no
matter what tomorrow. Price, say, a c
Financial Computation in
C/C+
04/05/17
1
Binomial Model
S (n, i ) S (0)(1 U ) i (1 D) n i
at step n and node i,
where S(0) > 0, U > D > -1
and n >= i >= 0
04/05/17
2
Cox-Ross-Rubinstein (CRR) procedure
At the expiry date N, H(N, i) = h(S(N,i), for each no
Financial Applications Using Data
Structures and Templates
04/05/17
1
Overview
Introduce advanced object-oriented programming
techniques and demonstrate how these techniques could
be applied to solve complicated problems in quantitative
finance.
Impleme
Monte Carlo Methods
04/05/17
1
Overview
Path-dependent Options
Valuation
Pricing Error
Greek Parameters
Variance Reduction
Path-dependent Basket Options
04/05/17
2
Path-dependent Options
A money account:
A(t) = ert , where t 0 is the time, r R is the ris
Working with Historical & Market Data
04/05/17
1
Topics in Working with Historical & Market Data:
Access Market Data using libcurl in C+
Communicate between C+ and Excel
2
04/05/17
Access Market Data using libcurl in C+
libcurl - the multiprotocol file
Implementation of Non-linear
Solvers in C+
04/05/17
1
Overview
Implied volatility
Well-known numerical methods for solving non-linear
equations:
Bisection Method
Newton-Raphson Method
Three implementations of these methods:
Function pointers
Virtua
Financial Trading System Development
04/05/17
1
Automated Trading Systems (1/2)
An automated trading system consists of:
Interacting trade execution algorithms
Quantified trade selection rules
Business logic necessary to enter into and exit from
positi
Quantitative methods, Weeks 4-5: A basic
introduction to stochastic processes
Agn`es Tourin
October 18, 2016
1
Introduction
Stochastic processes are used for modeling the time evolution of financial
assets. In the course of the past 3 lectures, we have al
Quantitative methods, week 10: A basic
introduction to stochastic calculus and its
application to the modeling of dynamic asset
prices
Agn`es Tourin
January 3, 2016
1
Introduction
The aim of this lecture is to introduce in an elementary manner the most
ba
Quantitative methods,
Weeks 13-14: one period investment models
and the connection with the risk-neutral
probability measure
Agn`es Tourin
October 18, 2015
1
Single period consumption and investment
problems
In this lecture, I draw heavily from the textbo
Quantitative methods, week 3: Markov chains
Agn`es Tourin
September 27, 2016
1
1.1
Markov chains
Introduction
This week, we study Markov chains. This study is motivated by the numerous applications to Insurance and Finance, in particular to credit risk
bu