The analytical finance package
We describe the Analytical Finance Package, a set of Java applets which is developing at the Malardalen University.
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irk-123456789-45242009-11-25T12:00:31Z The analytical finance package Silvestrov, D. Malyarenko, A. We describe the Analytical Finance Package, a set of Java applets which is developing at the Malardalen University. 2007 Article The analytical finance package / D. Silvestrov, A. Malyarenko // Theory of Stochastic Processes. — 2007. — Т. 13 (29), № 4. — С. 201–209. — Бібліогр.: 13 назв.— англ. 0321-3900 http://dspace.nbuv.gov.ua/handle/123456789/4524 en Інститут математики НАН України |
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We describe the Analytical Finance Package, a set of Java applets which is developing at the Malardalen University. |
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Silvestrov, D. Malyarenko, A. |
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Silvestrov, D. Malyarenko, A. The analytical finance package |
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Silvestrov, D. Malyarenko, A. |
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Silvestrov, D. |
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The analytical finance package |
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The analytical finance package |
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The analytical finance package |
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The analytical finance package |
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The analytical finance package |
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analytical finance package |
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Інститут математики НАН України |
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2007 |
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The analytical finance package / D. Silvestrov, A. Malyarenko // Theory of Stochastic Processes. — 2007. — Т. 13 (29), № 4. — С. 201–209. — Бібліогр.: 13 назв.— англ. |
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AT silvestrovd theanalyticalfinancepackage AT malyarenkoa theanalyticalfinancepackage AT silvestrovd analyticalfinancepackage AT malyarenkoa analyticalfinancepackage |
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Theory of Stochastic Processes
Vol.13 (29), no.4, 2007, pp.201–209
DMITRII SILVESTROV AND ANATOLIY MALYARENKO
THE ANALYTICAL FINANCE PACKAGE
We describe the Analytical Finance Package, a set of Java applets
which is developing at the Mälardalen University.
1. Introduction
Analytical Finance is the research area that includes financial mathe-
matics, financial engineering, and financial and risk management software.
The Analytical Finance group was created by the Department of Mathe-
matics and Physics at the Mälardalen University in 1999. Research studies
of the group are concentrated in the above mentioned domains and in some
related research areas such as actuarial mathematics, optimisation, applied
statistics and stochastic processes, computational game theory, simulation,
scientific computing, informatics.
The development of the pilot financial and risk management software
projects is one of the main research area of the Analytical Finance Group.
In this paper, we describe a project “Analytical Finance Package”.
The Analytical Finance Package is a library of applets in the area of
Analytical Finance. The project was initiated in 2003, and is developing
on a permanent base. The library is free software and consists mainly of
the applets written by the students as their seminar reports, bachelor and
master theses. You can find the applets and their documentation on the
Web page [1]. In order to make your browser adapted for running applets,
you may need to download the Java Runtime Environment for your platform
from http://java.sun.com.
The applets are divided into three groups: A Simulation of pricing
processes; B Estimation of pricing processes; C Evaluation of financial con-
tracts.
In what follows, we will describe the library in more details.
Invited lecture.
2000 Mathematics Subject Classifications. 62P05.
Key words and phrases. Analytical finance, applet, Java, stochastic simulation.
201
202 DMITRII SILVESTROV AND ANATOLIY MALYARENKO
2. Simulation of pricing processes
The students of the program “Analytical finance” who studied Java in
2004, have written applets concerning computer simulation of stochastic
processes. The resulting applets are:
1. Applet A01: Autoregressive model, by Krasimira Kirova and Ying
Ni. This applet simulates the autoregressive model of order 4, where
the logarithmic returns hn are hn = a0 + a1hn−1 + a2hn−2 + a3hn−3 +
a4hn−4 + σεn, with some constants a0, a1, a2, a3, a4, and σ0, where
εn is the sequence of independent standard normal random variables.
Ying Ni is currently a PhD student of the Department of Mathematics
and Physics.
2. Applet A02: Jump-diffusion model, by Robin Lundgren. This applet
simulates the Merton jump-diffusion model:
S(t) = S(0) exp
⎧⎨
⎩(μ − σ2/2 − λν)t + σW (t) +
N(t)∑
j=1
Yj
⎫⎬
⎭ ,
where the Wiener process W (t), the Poisson process with intensity
λ, and the identically distributed random variables Yj are mutually
independent. Later on, this project was extended to the master thesis.
Robin Lundgren is currently a PhD student of the Department of
Mathematics and Physics.
3. Applet A03: Standard user interface for simulation applets, by Xin
Mai and Weiss Amani. The authors created a user interface for simula-
tion applets. It contains simulation of standard Cox–Ross–Rubinstein
model and pricing index controlled by Markov chain.
4. Applet A04: GARCH model, by Sona Gevorgyan, Enrike Barrientos
and Nahir Hanna. This applet simulates the Generalised Autoregres-
sive Conditional Heteroscedasticity model, where past observations of
the variance and variance forecast are used to predict future variances:
hn = σnεn with σ2
n = a0 +
∑p
j=1 ajh
2
n−j +
∑q
j=1 bjσ
2
n−j .
5. Applet A05: ARMA model, by Gao Jongjie and Rafael Cortes. This
applet simulates the ARMA model
hn = a0 +
∑p
j=1 ajhn−j +
∑q
j=1 bjεn−j + σεn.
6. Applet A06: GPI model, by Herve Fandom Tchomgouo. This applet
simulates trajectories of the pricing process controlled by global price
index,
hn = a0 +
p∑
j=1
ajhn−j +
q∑
j=1
bj h̃n−j + σnεn,
THE ANALYTICAL FINANCE PACKAGE 203
where h̃n is the pricing index generated by another sequence of in-
dependent standard normal random variables ε̃n, independent from
εn:
h̃n = a0 +
q∑
j=1
ãj h̃n−j + cnε̃n.
7. Applet A07: Stochastic volatility model, by Daniela Andersson and
Zheng Wang. This applet simulates the following model:
hn = σnεn,
where
σn = exp[(a0 + a1Δn−1 + . . . + apΔn−2 + cε̃n)]/2.
8. Applet A08: Cox–Ross–Rubinstein model, by Mazyar Rostami. This
now classical model is:
hn = εn ln λ,
where λ1 and εn is the sequence of independent and identically dis-
tributed Bernoullian random variables with
P{ε1 = 1} = p, P{ε1 = −1} = 1 − p, 0p1.
9. Applet A09: automaton model simulator, by Robert Byström. The
model under simulation is
hn = μi + σiεn, if In = i,
where In = 1, if hn−1Δ, In = 0, if |hn−1| ≤ Δ, and In = −1, if
hn−1 − Δ.
10. Applet A10: moving average model, by Alexander Svahn, David Hefner,
Jakob Wernroth and Jonas Gustavsson. The model is
hn = b0 + b1εn−1 + . . . + bqεn−q + σεn.
3. Solutions to some elementary exercises in mathematical
finance
The students of the program “Analytical finance” who studied Java in
2005, have written applets that solved some calculational exercises from [2].
The resulting applets are:
1. Applet C01: American options with dividends, by Ling Wang, Bing
Wang and Yanjun Wang. Solves exercises 7.1–7.3.
204 DMITRII SILVESTROV AND ANATOLIY MALYARENKO
2. Applet C03: pricing European options by binomial model method, by
Tina Vedenpää and Cecilia Flink. Solves exercises 5.1–5.2.
3. Applet C04: pricing European call options on a forward contract,
by Mahsima Ranjbar, Malin Andersson and Cecilia Isaksson. Solves
exercises 7.7–7.9.
4. Applet C05: binomial pricing of European put options with replica-
tion, by Armand Fotsing, Hamadou Hamaounde, David Wellton, Basil
Wakid Hassan and Ren Minyi. Solves exercises 5.8–5.9.
5. Applet C06: replicating the stock in the binomial pricing model, by
Fred Takoeta. Solves exercise 5.6.
6. Applet C07: pricing American put options with replication, by Antti
Laine, Amir Kheirollah and Toma Boyacioglu. Solves exercises 7.4–
7.6.
7. Applet C09: bond price calculator, by Aminur Roshid, Isaac Acheam-
pong, Peter Agyemang-Mintah and Yue Song. Solves exercises 1.6–
1.10.
Later on, these applets were included in the Internet-based lecture notes
“Introduction to mathematical finance” by the second author.
4. Solutions to some problems from Institute of Actuaries
examination paper
The students of the program “Analytical finance” who studied Java in
2006, have written applets that solved some problems from Institute of
Actuaries examination papers [3]. The resulting applets are:
1. Applet C11: Eurobonds problem, by Kamila Giedrojc, Ewa Tropak
and Romans Obrezkovs. Examination 7 September 2005, subject
CT1 — Financial Mathematics Core Technical, exercise 6.
2. Applet C12: investor’s problem, by Elizabeta Tudzarovska, Izabela
Matusiak, Kwok-wai Choy, Sophia Abdi Hassan and Khadija Khapasi.
Examination 6 April 2005, subject CT1 — Financial Mathematics
Core Technical, exercise 7.
3. Applet C13: bond reselling problem, by Malgorzata Andros, Matti
Simperi and Piotr Liszewski. Examination 7 September 2005, subject
CT1 — Financial Mathematics Core Technical, exercise 10.
THE ANALYTICAL FINANCE PACKAGE 205
4. Applet C14: loan repayment applet, by Osei Benjamin Kwesi Amoako,
George Manteaw Anobah, Aleksandra Sroka and Jacek Zniszczo�l. Ex-
amination 6 April 2005, subject CT1 — Financial Mathematics Core
Technical, exercise 11.
5. Applet C15: insurance problem, by Beata Lubecka, Peter Malosha
Mayunga, Maziar Saei Aghmiouni and Marek Geringer De Oedenberg.
Examination 7 September 2005, subject CT1 — Financial Mathemat-
ics Core Technical, exercise 11.
5. Solutions to problems about calculation option prices by
finite difference methods
The students of the program “Analytical finance” who studied Java in
2007, have written applets that solved some exercises concerning calculation
option prices by finite difference methods from [4]. The resulting applets
are:
1. Applet C27: European Option Calculator, by Jie Zhang, Michael
Wennermo, Tatiana Ozhigova, Konrad Szczypkowski, Michail Musatov.
Solves exercise
2. Applet C28: Java Applet for pricing European options using implicit
finite-difference method, by Boyko Vasilev, Mbecho Techago, Hanney
Al-Qaisi, Viktor Taku-Mbi, Vitaliy Drozdenko.
3. Applet C29: Java Applet for pricing American options using projected
explicit finite-difference method, by Zhi Xu, Tian Tian, Wang Zheng,
Michail Kalavrezos, Mehmet Yasin Hürata.
4. Applet C30: Java Applet for the pricing of American options using the
implicit finite-difference method, by Dong Liang, Leonel Taku Ayuk,
Takura Muusha, and Coline Sume Emadione.
6. Bachelor theses
Several students of the Analytical Finance program have chosen to write
their bachelor theses using Java. Their applets are:
1. Applet C16: Pricing put options using explicit finite difference method
in Java graphical user interface, by Yue Song. The algorithm from [5,
pp. 92–95] was translated to Java, the graphical user interface was
written, the numerical experiments were performed.
2. Applet C18: Pricing futures using the two-period binomial model in
Java, by Minyi Ren and Wakid Hassan Basil. This study develops an
applet for binomial futures pricing.
206 DMITRII SILVESTROV AND ANATOLIY MALYARENKO
3. Applet C24: Monte Carlo Simulation of Bond Prices in the Ho and
Lee Model, by Sophia Abdi Hassan. The algorithm from [6] was re-
alised in Java, the graphical user interface was written, the numerical
experiments were performed.
4. Applet C26: Java Applet For The Closed Form Valuation Of American
Option Using Bjerksund and Stensland Model, by Mbecho Techago
Emmanuel. The algorithm from [7] was realised to Java, the graphical
user interface was written, the numerical experiments were performed.
We would like to describe Applet C26 in more details. Bjerksund and
Stensland [7] obtain an accurate and computer efficient lower approxima-
tion to the American option value by imposing a feasible but non-optimal
exercise strategy. In particular, they assume a flat early exercise boundary.
In [8], they divided time to maturity into two periods, each with a flat early
exercise boundary, and obtained even more accurate lower approximation.
They also suggested a reasonable approximation of the true option value,
twice the option value calculated by the two-step boundary method minus
the option value calculated by the flat boundary method.
Mbecho Techago Emmanuel realised all the three above described meth-
ods plus the binomial tree method in his applet and has written a graphical
user interface. A typical result of calculation is shown in Fig. 1.
7. Master theses
Several students of the Analytical Finance program have chosen to write
their master theses using Java. Their applets are:
1. Applet A11: Java Applet for the Pricing of Exotic Options by Monte-
Carlo Simulations in a Lèvy market with Stochastic Volatility, by
Isaac Acheampong. The algorithm from [9] was realised to Java, the
graphical user interface was written, the numerical experiments were
performed.
2. Applet C08: The Hull-White model, by Aminur Roshid. The algo-
rithm from [6] was realised in Java, the graphical user interface was
written, the numerical experiments were performed.
3. Applet C10: Simulation of the short interest rate in the Vasicek model,
by Natalia Spas’ka and Olexander Sheychenko. The algorithm from
[6] was realised in Java, the graphical user interface was written, the
numerical experiments were performed. The authors are currently
working in a big insurance company in Sidney.
THE ANALYTICAL FINANCE PACKAGE 207
Figure 1: Typical results of calculations in Applet C26
4. Applet C17: A Java program for pricing options using the trinomial
tree, by Youmbi Etien Kalame. An applet for options pricing was
written.
5. Applet C19: Pricing convertible bonds with Monte Carlo simulations,
by Cecilia Isaksson. The algorithm from [10] was realised in Java, the
graphical user interface was written, the numerical experiments were
performed. The author is currently working in a bank in Liechtenstein.
This work was continued in Applet C23 by Kateryna and Vladimir
Mishchenko. The results of their work are published in this volume.
6. Applet C20: A Java applet for credit risk estimation with Wishart
multivariate stochastic volatility, by Amoako Osei Benjamin Kwesi.
The algorithm from [11] was realised in Java, the graphical user inter-
face was written, the numerical experiments were performed.
7. Applet C21: A Java applet for pricing convertible bonds with credit
risk, by Charles Etang Ntui. The algorithm from [12] was realised in
Java, the graphical user interface was written, the numerical experi-
ments were performed.
208 DMITRII SILVESTROV AND ANATOLIY MALYARENKO
8. Applet C22: A Java applet for simulation of economy with borrowers
under costly defaults, by Basil Wakid Hassan. The algorithm from
[13] was realised in Java, the graphical user interface was written, the
numerical experiments were performed.
9. Applet C25: The Java applet for pricing put options by the implicit
finite difference method, by Wang Janjun. Several numerical finite
difference methods were realised in this applet.
Figure 2: Typical results of calculations in Applet A11
We would like to describe Applet A11 in more details. Schoutens and
Symens [9] price barrier, lookback and cliquet options by Monte-Carlo sim-
ulation in a stock price model based on Lévy processes with stochastic
volatility. The sampling of paths is based on a compound Poisson approxi-
mation of the Lévy process involved.
Isaac Acheampong realised this complicated model in Java. A typical
result of calculations is shown in Fig. 2.
8. Conclusions
In this paper, we have described the Analytical Finance Package, which
is creating by the students of the Analytical Finance program at the the
THE ANALYTICAL FINANCE PACKAGE 209
Mälardalen University under the authors’ supervision. In future, we plan to
further develop this useful programming tool and include several interesting
stochastic models of financial instruments.
References
1. URL:http://www.mdh.se/ima/personal/amo01/analyticalfinance/
af3.software/analytical-finance-package/, last visited September 19, (2007).
2. Jarrow, R.A., Turnbull, S.M. Derivative securities, second edition, Thom-
son Learning, (2000), ISBN 0-538-87740-5.
3. URL:http://www.actuaries.org.uk/Display Page.cgi?url=/students/
specimen papers.xml, last visited September 26, (2007).
4. You–Ian Zhu, Xiaonan Wu, I–Liang Chern, Derivative Securities and Dif-
ference Methods, Springer, New York, (2004), ISBN 0–387–20842–9.
5. Ødegaard, B. A., Financial Numerical Recipes in C++, http://finance-
old.bi.no/ bernt/gcc prog/recipes/recipes/ last modified April 6, (2005).
6. Glasserman, P., Monte Carlo methods in financial engineering, Springer,
Berlin, (2003).
7. Bjerksund, P., Stensland, G., Closed-form approximation of American op-
tions, Scand. J. Management, 9, Suppl., S88–S99.
8. Bjerksund, P., Stensland, G., Closed form valuation of American options,
Working paper, (2003).
9. Schoutens, W., Symens, S., The pricing of Options by Monte Carlo simu-
lations in a Lèvy Market with Stochastic Volatility, Int. J. Theor. Appl.
Finance, 6(8),(2003), 839–864.
10. Amman, M., Kind, A, Wilde, C., Simulation-Based Pricing of Convert-
ible Bonds, Working paper, University of St.Gallen / Goethe University
Frankfurt, (2005).
11. Gouriéroux, C., Sufana, R., Derivative Pricing with Wishart Multivariate
Stochastic Volatility: Application to Credit Risk, Working paper, University
of Toronto, (2005).
12. Ayache, E., Forsyth, P.A, Vetzal, K.R., The valuation of convertible bonds
with credit risk, J. Derivatives, 11 (2003), 9–29.
13. Basak, S., Shapiro, A., A model of credit risk, optimal policies and asset
prices, J. Business, 78 (2005), 1215–1266.
Department of Mathematics, Mälardalen University, Box 883,
SE-72123, Väster̊as, Sweden
E-mail: dmitrii.silvestrov@mdh.se, anatoliy.malyarenko@mdh.se
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