Ph.D. Thesis Outline
Alexander Petrov
“Financial Markets Reorganisation and Derivatives Valuation in Central
and Eastern Europe”
Aleksander Petrov
Supervisor Prof. Dr. Josef Zechner
Co-Supervisor Prof. Dr. Robert Tompkins
The Ph.D. Thesis will be in the form of two - three separate essays:
Essay No.1 Working Title: “Comparative Analysis of Objective Dispersion
Processes in Established and Emerging European Stock Markets”
Essay Overview
I. Aim:
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compare stock indices of established and emerging markets (statistical characteristics)
calculate correlations and test for changing correlation patters in time
test alternative models to explain objective dispersion
find a realistic price process based on jump processes and stochastic volatility
analyze reasons for difference in estimated models between the two groups of markets
II. Data:
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The established markets are represented by the following four indices: S&P 500,
FTSE, Nikkei 225 and DAX. For each of them, both the cash index and the index
futures time series are available.
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The four Eastern European stock markets surveyed in the paper are Hungary, Czech
Republic, Poland and Russia. The paper looks at the USD-based indices traded on the
Vienna Stock Exchange, i.e. HTX (Hungarian Traded Index), CTX (Czech Traded
Index), PTX (Polish Traded Index) and RTX (Russian Traded Index), as well as the
local indices denominated in home currencies, i.e. BUX, WIG20, PX50 and RTS.
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The time period is January 3, 1995 – March 9, 2000 for all 8 markets.
III. Analysis -The paper compares the available series in the following way:
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Western cash indices vs. USD-based Emerging market indices
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Western cash indices vs. western index futures series – Futures prices have many
desirable properties: transform any non-traded asset into traded asset, take account of
dividends, solve the problem of asymmetric data and provide insights into the nature of
risk neutral distributions (based on the assumption of complete markets). However,
while western markets are futurised and data is available, eastern markets have
extremely illiquid futures exchanges. This analysis tests whether there are any
systematic differences in the statistical properties of the cash vs. futures indices in the
west. If the initial expectation of no major differences is confirmed, then the result can
be later used in Essay 2, when valuing derivatives under the Q-measure.
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Eastern USD-based vs. Eastern local – the difference between the two is the currency
return.
Ph.D. Thesis Outline
Alexander Petrov
Essay Structure
I. Introduction
II. Literature Preview
III. Returns’ statistical characteristics – this paper will motivate the use of seven characteristics
to describe the non-normality of unconditional daily return distributions in the eight markets:
1. Skewness
2. Kurtosis
3. Volatility – critical for later models of derivatives. The paper will use the volatility
cone approach developed by Burghardt & Lane ’90 - representation of realized
historical volatilities. The basis for comparison between the markets is the Coefficient
of Variation (CoV).
4. Leverage effect – correlation between price levels and volatility levels
5. Variability of Volatility (decay) – to measure time varying dynamics of the standard
deviation of volatility.
6. Short term Autocorrelation – average autocorrelation of absolute returns for the lagged
periods from the 1st to the 20th lag to describe clustering.
7. Long-term autocorrelation – lagged periods from the 50th to the 70th lag.
IV. Alternative Models – test for alternative models describing the unconditional price processes:
1. GBM i.i.d. – Black Scholes assumptions hold; rejected by the data
2. Models of stochastic volatility (GARCH)– can not capture excessive kurtosis
3. Fat tails models (Stable Paretian / Mandelbrot’ 63) – how to incorporate with varying
volatility
4. Models combining stochastic volatilities with fat tail (excessive kurtosis) distributions:
 D. Bates
 L. Scott
 P. Schoenbucher
 Conditional Heteroscedasticity and Jumps / Ho, Perraudin, Sorensen
 Normal Inverse Gaussian / R. Tompkins
 Non-Gaussian processes of Ornstein-Uhlenbeck type / O. Nielsen & N. Shephard
V. Empirical Results
 Use a version of the sample generalized method of moments (Gallant and Tauchen ’96)
as a method of fitting
 Parameter values of alternative models estimated by simulation
VI. Results analysis
 Searching for significant improvement in explaining the price process dynamics
 Results: Does the model capture price dynamics?
 If yes, why? => use it as a building block for Essay No.2
 If not fully, why? => use it as a building block to essay No.3
- Credit risk
- Liquidity risk
- Fractionalisation and segmentation
- Transaction costs
- Others ?
VII. Conclusions
Ph.D. Thesis Outline
Alexander Petrov
Essay No.2 – Options (ideas)
Aim:
- once a realistic price process is found => apply it to options pricing
Possible problems:
- hardly any data on Emerging Europe’s derivatives markets
- how to achieve standartisation of option prices across markets
- risk neutrality (priced under the Q – measure)
Simulation procedures: Monte Carlo Simulations vs. STELLA Model
What is STELLA? - STELLA® is a user-friendly software, which uses graphical
representation of a system of differential equations, thus allowing for creation of a dynamic
model. As such, it is particularly applicable for modeling chaos. Furthermore, its graphical
interface allows for the inclusion of any kind of explanatory variable helping to visualise the
whole model. Used extensively in the MIT.
Option prices vs. implied volatilities: => Idea: Express simulated prices as implied volatilities
in order to enable graphical representation and comparisons.
Steps:
Compute real volatility smiles for Developed Markets from the data
Compute simulated volatility smiles from the model specified in Essay 1
Compare the results – similar, systematically different, unsystematically different ?
If similar – excellent model => brave expectations
If systematically different => model is unable to fully understand the behavior of implied
volatility surfaces. The possible difference between the two may be attributed to:
- risk premiums
- transaction costs
- illiquidity
- wrong functional form
- distributions
- market frictions
If unsystematical difference – not a lot more can be said
In the case of systematic difference the essay will test the following hypothesis:
The difference between the simulated and actual volatility surfaces in the case of the Emerging
European Markets is the same as the difference in the Developed Markets
Compute simulated option prices using model from essay1 and STELLA simulation
Add the difference in volatility surfaces estimated from developed markets
Compare the result with actual data from the only well-functioning derivatives Exchange in
CEE – Hungary.
If results are similar => a major breakthrough in understanding option valuations in Emerging
Europe. Conclusions can be made of model applicability to other countries.
If there is a difference (in the case of one market only, one can not speak of systematic v.s.
unsystematic) => failure of model to fully describe option pricing. May be caused by:
- improper pricing models, market imperfections, others
The idea of how the above might be addressed will be the aim of Essay 3.
Ph.D. Thesis Outline
Alexander Petrov
Essay No.3 – Regulation and Reorganisation (ideas)
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How are Stock Exchanges regulated?
Rules of listing, types of companies
Rationale for existence
New trends and ideas