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Pl find Below attached Syllabus for CQF Exam for your ready references :

CQF Syllabus mentioned below :
Random Behaviour of Assets
Different types of financial analysis
• Examining time-series data to model returns
• Are prices random?
• The need for probabilistic models
• The Wiener process, a mathematical model of randomness
• The lognormal random walk—The most important model for
equities, currencies, commodities and indices

Transition Density Functions
• A Brownian motion
• A trinomial random walk
• Transition density functions
• Our first differential equation
• Similarity solutions

Stochastic Calculus and Itˆo’s Lemma
Stochastic calculus is very important in the mathematical mod-
eling of financial processes. This is because of the underlying
(assumed) random nature of financial markets.

Simulating and Manipulating Stochastic Differential Equations
Using Itˆo’s lemma to manipulate stochastic differential equa-tions
• Continuous-time stochastic differential equations as discrete-
time processes

• Simple ways of generating random numbers in Excel
• Correlated random walks

Binomial Model
a simple model for an asset price random walk
• delta hedging
• no arbitrage
• the basics of the binomial method for valuing options
• risk neutrality

Stochastic Calculus Toolbox, Part II Martingales
we talk about martingales:
I What is a martingale?
I Martingales and Itˆo calculus
I Martingale unmasked: how do I know if my stochastic process
is a martingale?
I Exponential martingales, Girsanov and change of measure

Euler discretization of SDE
Consider Geometric Brownian Motion (GBM) as a model for the dynamics
of a financial asset: dS = μSdt + σSdW (1)
This asset could be the price of a share of company. Using Euler dis-
cretization compute one potential future path for the evolution of the as-
set for a period of one week (Mon thru Fri). Consider a flat interest rate
of 5% pa and a volatility of 30 % pa. The initial price (as observed to-
day) is S0=100 USD on Monday EOD. Use a pre-computed vector of ran-
dom numbers (samples from a standard normal distribution) composed of

1 = +0.4423,2 = −0.1170,3 = +0.0291,4 = +0.6872.
2 Monte Carlo Simulation
We would like to price a six-month European Call option on Vodafone equity
(VOD). The current equity price of Vodafone is 100 USD, with a volatility 1
of 20 percent and a strike of 100 USD. We assume that the stock pays no
dividends. The current interest risk-free rate is 5 percent pa. Assume that
we are given the following pre-computed five trajectories, in the table below,
based on using GBM. Each line contains the values of the assets and the
random samples used. What is the price of the premium of this option using
MC simulation?

Financial Regulation and Basel III
“Currently, every European bank must observe approximately 40,000 legally binding
requirements of the European Union. In the field of banking
supervision, four thousand and one different rules have been set
down on 34,019 pages … Today it is almost impossible to find any
banking supervisor or bank practitioner who is able to explain exactly
the supervisory rules and their consequences. The scope and
complexity of the rules are just too great.”

Value at Risk and Expected Shortfall
risk management is the identification, assessment, and prioritization of risks
followed by coordinated and economical application of resources to minimize,
monitor, and control the probability and/or impact of unfortunate events or to
maximize the realization of opportunities.

Fundamentals of Optimization and Application to Portfolio Selection
how to formulate an optimization problem;
I elementary rules and tips.
II. Unconstrained Optimization Problems
I how to use calculus to solve unconstrained optimization problems;
I application to mean-variance optimization;
I application to linear regression.

III. Optimization problems with equality constraints
I the method of Lagrange;
I application to portfolio selection;
I the minimum variance portfolio;
I the tangency portfolio.

IV. The Black-Litterman model.

V. A short note on optimization problems with inequality constraints: the
Kuhn-Tucker conditions.

Asset Returns: Key, Empirical Stylized Facts
Know about the most important empirical properties of asset returns,
• Know that changes in volatility explain many empirical effects,
• Have seen several examples of time series,
• Have seen several examples of autocorrelations.

Volatility Models: the ARCH framework
Know there are many ways to define volatility,
• Know why ARCH models are often estimated from daily price series,
• Appreciate that estimating ARCH models and volatilities is straightforward,
• Have seen simple equations for predicting volatility,
• Realize that stock index volatility generally moves in the opposite direction to
the index.

Liquidity Asset Liability Management
Bear Stearns & Co., the fifth-largest U.S. investment bank as 2008 began,
burned through nearly all of its $18 billion in cash reserves during the week
of March 10, 2008.
• Bear survived to the dose of business on Friday, March 14 only because of
that morning’s groundbreaking announcement: the Federal Reserve Bank
of New York, using JP Morgan Chase & Co. as a conduit, would provide
Bear with secured financing for a period of up to 28 days.
• Despite this unprecedented provision of liquidity support from the Federal
Reserve System to an investment bank, it was insufficient to reverse
Bear’s condition, and on Friday evening, Bear CEO Alan Schwartz learned
Bear’s access to the N.Y. Fed’s new lending facility would last only one day.

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