|
[published papers |
working papers |
miscellaneous]
|
|
|
Anatoliy Swishchuk
|
2005
|
|
Modelling and pricing
of variance swaps for stochastic volatilities with delay.
|
[pdf]
|
|
WILMOTT Magazine,
September 2005, Issue 19, pp. 63-73.
|
|
Abstract
Variance swaps for financial markets with underlying asset and stochastic
volatilities with delay are modelled and priced in this paper. We found some
analytical close forms for expectation and variance of the realized continuously
sampled variance for stochastic volatility with delay both in stationary
regime and in general case. The key features of the stochastic volatility model
with delay are the following: i) continuous-time analogue of discrete-time
GARCH model; ii) mean-reversion; iii) contains the same source of randomness
as stock price; iv) market is complete; v) incorporates the expectation
of log-return. We also present an upper bound for delay as a measure of risk.
As applications, we provide two numerical examples using S&P60 Canada
Index (1998-2002) and S&P500 Index (1990-1993) to price variance swaps
with delay. Varinace swaps for stochastic volatility with delay is very similar
to variance swaps for stochastic volatility in Heston model, but simplier to
model and to price it.
|
|
|
Anatoliy Swishchuk
|
2004
|
|
Modeling of variance and volatility swaps for
financial markets with stochastic volatilities
|
[pdf]
|
|
WILMOTT Magazine,
September Issue, Technical Article No 2, pp. 64-72.
|
|
Abstract
In this paper I proposed a new probabilistic approach based on change of
time method to study variance and volatility swaps for financial markets
with underlying asset and variance that follow the Heston (1993) model.
Covariance and correlation swaps for the financial markets have also been
studied. As an application, a numerical
example using S&P60 Canada Index to price swap on the volatility was
provided.
|
|
|
Christiane Lemieux
|
2004
|
|
Randomized quasi-Monte Carlo: a tool for improving the efficiency
of simulations in finance
|
|
|
Proceedings of the 2004 Winter Simulation Conference,
IEEE Press, to appear.
|
|
|
R. Chen et al.
|
2002
|
|
Price pseudo-variance,
pseudo-covariance, pseudo-volatility and pseudo-correlation swaps in
analytical closed form
|
[pdf]
|
|
Proceedings of the Sixth PIMS Industrial
Problems Solving Workshop, PIMS IPSW 6, University of British Columbia,
Vancouver, Canada, May 27-3. Editor: J. Macki, University of Alberta,
Canada, June, 2002, pp.45-55.
|
|
Abstract
Some expressions for price of the realised discrete sampled variance
$Var_n(S):=\frac{n}{(n-1)T}\sum_{i=1}^{n}\log2\frac{S_{t_{i}}}{S_{t_{i-1}}},$
(or pseudo-variance) were obtained.
|
|
|
Len Bos, Tony Ware and Boris Pavlov
|
2002
|
|
On a semi-spectral method for pricing an option on a mean-reverting asset
|
[web]
|
|
Quantitative Finance, Volume 2, pp. 337-345
|
|
Abstract
We consider a risky asset following a mean-reverting stochastic
process of the form $dS = \alpha (L-S) dt + \sigma S dW$. We show that the
(singular) diffusion equation which gives the value of a European
option on S can be represented, upon expanding in Laguerre
polynomials, by a tridiagonal infinite matrix. We analyse this matrix
to show that the diffusion equation does indeed have a solution and
truncate the matrix to give a simple, highly efficient method for the
numerical calculation of the solution.
|
|
|
Len Bos and Tony Ware
|
2001
|
|
How to solve multi-asset Black-Scholes with time-dependent
volatility and correlation
|
|
|
Journal of Computational Finance, 4(2):99--107, Winter 2001
|
|
| Ali Lari-Lavassani Mohammedreza Simchi and Tony Ware |
2001 |
| A discrete valuation of swing options
|
|
|
Canadian Applied Mathematics Quarterly, 9(1):35--74, Spring 2001
|
|
Abstract A discrete forest methodology is developed for swing options as a
dynamically coupled system of European options. Numerical
implementation is fully developed for one- and two-factor, mean-reverting,
underlying processes, with application to energy markets.
Convergence is established via finite difference
methods. Qualitative properties and sensitivity analysis are considered.
|
|
| Ali Lari-Lavassani and Bradley Tifenbach |
2001 |
|
A general framework for trinomial trees
|
|
|
Proceedings of the 2001 International Conference
on Computational Science (ICCS 2001), Springer-Verlag Lecture
Notes in Computer Science, Volume 2073.pp. 597-606.
|
|
Abstract Three general trinomial option pricing methods are formally
developed and numerically implemented and explored.
Applications to American option pricing are presented for one and two factor models.
|
|
|
Ali Lari-Lavassani, Ali A. Sadeghi and Tony Ware
|
2001
|
|
Modelling and implementing mean reverting price processes in energy markets
|
[pdf]
|
|
Electronic Publications of the International Energy Credit Association (www.ieca.net).
|
|
Abstract Various one to three factor mean reverting processes are investigated
in the context of energy markets. Results of natural gas and crude oil market data calibrations
are presented. Numerical implementations of the multifactor models are discussed via binomial
trees, a finite difference method and Monte Carlo simulation.
|
|
|
Christiane Lemieux and P. L'Ecuyer
|
2001
|
|
On the use of quasi-Monte Carlo methods in computational finance
|
|
|
Computational Science ICCS 2001 (part I), Lecture Notes in Computer Science vol. 2073, Springer, 607 - 618, 2001.
|
|
|
R. J. Griego and A. V. Swishchuk
|
2000
|
| A Black-Scholes formula for a
securities markets in random environment
|
[pdf]
|
| Theory Probab. Math. Statist., No. 62., 9-18.
|
|
Abstract
We consider (B,S)-security market (consisting of bond and stock) with
interest rates, appreciation rate and volatility depending on some Markov
process.
We derive the Black-Scholes formula for this security market in Markov
random environment.
|
|
|
A. V. Swishchuk and A. V. Kalemanova
|
1999
|
|
Stochastic stability of interest rates with jumps
|
[pdf]
|
| Theory Probab. Math. Statist., No. 61,
161-172.
|
|
Abstract
Stochastic stability of interest rates (Vasicek, Cox-Ingersoll-Ross (CIR)
and generalized CIR models) and their generalization on the case of
existence of jump random changes is studied in this chapter.
|
|
|
H. Ben Ameur, P. L'Ecuyer and Christiane Lemieux
|
1999
|
|
Variance reduction of Monte Carlo and randomized quasi-Monte Carlo estimators for stochastic volatility models in finance
|
|
|
Proceedings of the 1999 Winter Simulation Conference, IEEE Press, December 1999, 632-639.
|
|
