Working Papers

The WNE Working Papers series has been published by the Faculty of Economic Sciences at the University of Warsaw since 2008.

The WNE Working Papers series provides a fast, open channel for disseminating research conducted at the Faculty of Economic Sciences, University of Warsaw. The papers hosted here are working versions (pre-prints) and may evolve as authors refine their analyses, incorporate feedback, or progress through formal peer-review. What you read is the current version released by the authors, timestamped and assigned DOI/ISSN identifiers to ensure precise citation and version tracking. Copyright remains with the authors, who may, at any time, upload a revised file or add a note directing readers to a later, peer-reviewed publication.

The Working Papers series accepts articles by research employees of the Faculty and publications from conferences organised at the Faculty of Economic Sciences at the University of Warsaw. Articles should be original research papers which have not been previously published, on the subject of economics.

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Number of Results 7

WP(20/2026)514. Hedging Auction Volatility with Gap Call Options

Authors: Mbara Gilbert
We investigate the feasibility of hedging commodity price risk using gap call options within an auction-based market devoid of traditional derivatives. Using a novel, high-frequency dataset from the Nairobi Coffee Exchange (NCE), we model spot price …

WP514. Hedging Auction Volatility with Gap Call Options

We investigate the feasibility of hedging commodity price risk using gap call options within an auction-based market devoid of traditional derivatives. Using a novel, high-frequency dataset from the Nairobi Coffee Exchange (NCE), we model spot price dynamics by deriving a Geometric Brownian Motion process from the independent private values paradigm. The estimated model captures the unique microstructure of the NCE, where discrete weekly auctions generate prices characterized by extreme volatility (146.5% annualized). We utilize Monte Carlo simulation to price and evaluate the performance of gap call options for buyers seeking protection against catastrophic price spikes. Our results demonstrate that gap options – characterized by a trigger price higher than the strike – provide superior risk-adjusted returns compared to standard European calls. Our study offers a practical framework for developing tailored risk management instruments in emerging commodity exchanges, and provides empirical evidence for the viability of gap options as a cost-effective hedging tool in high-volatility, institutionally constrained markets.


DOI: https://doi.org/10.33138/2957-0506.2026.20.514
Mbara Gilbert
risk management hedging commodity price risk gap options Nairobi Coffee Exchange geometric Brownian motion Monte Carlo simulation

WP(31/2020)337. Variance Gamma Model in Hedging Vanilla and Exotic Options

Authors: Bollin Bartłomiej, Ślepaczuk Robert
The aim of this research is to explore the performance of different option pricing models in hedging the exotic options using the FX data. We analyze the narrow class of Lévy processes - the Variance Gamma process in hedging vanilla, Asian and…

WP337. Variance Gamma Model in Hedging Vanilla and Exotic Options

The aim of this research is to explore the performance of different option pricing models in hedging the exotic options using the FX data. We analyze the narrow class of Lévy processes - the Variance Gamma process in hedging vanilla, Asian and lookback options. We pose a question of whether or not using additional level of complexity, by introducing more sophisticated models, improves the effectiveness of hedging options, assuming that hedging errors are measured as the differences between portfolio values according to the model and not real market data (which we don't have). We compare this model with its special case and the Black-Scholes model. We use the data for EURUSD currency pair assuming that option prices change according to the model (as we don't observe them directly). We use Monte Carlo methods in fitting the model's parameters. Our results are not in line with the previous literature as there are no signs of the Variance Gamma process being better than the Black-Scholes and it seems that all three models perform equally well.


Bollin Bartłomiej, Ślepaczuk Robert
Monte Carlo option pricing Variance Gamma BSM model Lévy processes FX market hedging Asian and lookback options

WP(28/2020)334. Value-at-risk — the comparison of state-of-the-art models on various assets

Authors: Kielak Karol, Ślepaczuk Robert
This paper compares different approaches to Value-at-Risk measurement based on parametric and non-parametric approaches. Three portfolios are taken into consideration — the first one containing only stocks from the London Stock Exchange, the se…

WP334. Value-at-risk — the comparison of state-of-the-art models on various assets

This paper compares different approaches to Value-at-Risk measurement based on parametric and non-parametric approaches. Three portfolios are taken into consideration — the first one containing only stocks from the London Stock Exchange, the second one based on different assets of various origins and the third one consisting of cryptocurrencies. Data used cover the period of more than 20y. In the empirical part of the study, parametric methods based on mean-variance framework are compared with GARCH(1,1) and EGARCH(1,1) models. Different assumptions concerning returns' distribution are taken into consideration. Adjustment for the fat tails effect is made by using Student t distribution in the analysis. One-day-ahead 95%VaR estimation is then calculated. Thereafter, models are validated using Kupiec and Christoffersen tests and Monte Carlo Simulation for reliable verification of the hypotheses. The overall goal of this paper is to establish if analyzed models accurately estimate Value-at-Risk measure, especially if we take into account assets with various returns distribution characteristics.


Kielak Karol, Ślepaczuk Robert
risk management Value-at-Risk GARCH models returns distribution Monte Carlo Simulation asset class cryptocurrencies

WP(18/2017)247. Simulation error in maximum likelihood estimation of discrete choice models

Authors: Czajkowski Mikołaj, Budziński Wiktor
Maximum simulated likelihood is the preferred estimator of most researchers who deal with discrete choice. It allows estimation of models such as mixed multinomial logit (MXL), generalized multinomial logit, or hybrid choice models, which have now be…

WP247. Simulation error in maximum likelihood estimation of discrete choice models

Maximum simulated likelihood is the preferred estimator of most researchers who deal with discrete choice. It allows estimation of models such as mixed multinomial logit (MXL), generalized multinomial logit, or hybrid choice models, which have now become the state-of-practice in the microeconometric analysis of discrete choice data. All these models require simulation-based solving of multidimensional integrals, which can lead to several numerical problems. In this study, we focus on one of these problems – utilizing from 100 to 1,000,000 draws, we investigate the extent of the simulation bias resulting from using several different types of draws: (1) pseudo random numbers, (2) modified Latin hypercube sampling, (3) randomized scrambled Halton sequence, and (4) randomized scrambled Sobol sequence. Each estimation is repeated up to 1,000 times. The simulations use several artificial datasets based on an MXL data generating process with different numbers of individuals (400, 800, 1200), different numbers of choice tasks per respondent (4, 8, 12) and different experimental designs (D-optimal, D-efficient for the MNL and D-efficient for the MXL model). Our large-scale simulation study allows for comparisons and drawing conclusions with respect to (1) how efficient different types of quasi Monte Carlo simulation methods are and (2) how many draws one should use to make sure the results are of "satisfying" quality – under different experimental conditions. Our study is the first to date to offer such a comprehensive comparison.


DOI: https://doi.org/10.26405/WP/WNE/2017/247/018
Czajkowski Mikołaj, Budziński Wiktor
discrete choice mixed logit simulated maximum log-likelihood function simulation error draws quasi Monte Carlo methods MLHS Halton Sobol number of draws

WP(32/2013)117. Robust estimation of the Pareto index: A Monte Carlo Analysis

Authors: Brzeziński Michał
The Pareto distribution is often used in many areas of economics to model the right tail of heavy-tailed distributions. However, the standard method of estimating the shape parameter (the Pareto index) of this distribution the maximum likelihood esti…

WP117. Robust estimation of the Pareto index: A Monte Carlo Analysis

The Pareto distribution is often used in many areas of economics to model the right tail of heavy-tailed distributions. However, the standard method of estimating the shape parameter (the Pareto index) of this distribution the maximum likelihood estimator (MLE) is non-robust, in the sense that it is very sensitive to extreme observations, data contamination or model deviation. In recent years, a number of robust estimators for the Pareto index have been proposed, which correct the deficiency of the MLE. However, little is known about the performance of these estimators in small-sample setting, which often occurs in practice. This paper investigates the small-sample properties of the most popular robust estimators for the Pareto index, including the optimal B-robust estimator (OBRE) (Victoria-Feser and Ronchetti, 1994, The Canadian Journal of Statistics 22: 247-258), the weighted maximum likelihood estimator (WMLE) (Dupuis and Victoria-Feser, 2006, Canadian Journal of Statistics 34: 639-658), the generalized median estimator (GME) (Brazauskas and Serfling, 2001a, Extremes 3, 231-249), the partial density component estimator (PDCE) (Vandewalle et al., 2007, Computational Statistics & Data Analysis 51: 6252-6268), and the probability integral transform statistic estimator (PITSE) (Finkelstein et al., 2006, North American Actuarial Journal 10, 1-10). Monte Carlo simulations show that the PITSE offers the desired compromise between ease of use and power to protect against outliers in the small-sample setting. 


Brzeziński Michał
Pareto distribution Pareto index power-law distribution robust estimation Monte Carlo simulation small-sample performance

WP(13/2012)79. Small sample properties of matching with caliper

Authors: Strawiński Paweł
A caliper mechanism is a common tool used to prevent from inexact matches. The existing literature discusses asymptotic properties of matching with caliper. In this simulation study we investigate properties in small and medium sized samples. We show…

WP79. Small sample properties of matching with caliper

A caliper mechanism is a common tool used to prevent from inexact matches. The existing literature discusses asymptotic properties of matching with caliper. In this simulation study we investigate properties in small and medium sized samples. We show that caliper causes a significant bias of the ATT estimator and raises its variance in comparison to one-to-one matching.


Strawiński Paweł
propensity score matching caliper Monte Carlo experiment finite sample properties

WP(25/2011)65. Dynamic caliper matching

Authors: Strawiński Paweł
Matched sampling is a methodology used to estimate treatment effects. A caliper mechanism is used to achieve better similarity among matched pairs. We investigate finite sample properties of matching with calipers and propose a slight modification to…

WP65. Dynamic caliper matching

Matched sampling is a methodology used to estimate treatment effects. A caliper mechanism is used to achieve better similarity among matched pairs. We investigate finite sample properties of matching with calipers and propose a slight modification to the existing mechanism. The simulation study compares the performance of both methods and shows that a standard caliper performs well only in case of constant treatment or uniform propensity score distribution. Secondly, in a case of non-uniform distribution or non-uniform treatment the dynamic caliper method outperforms standard caliper matching.


Strawiński Paweł
propensity score matching caliper efficiency Monte Carlo study finite sample properties
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