Talks (Selected Conference/Seminar Presentations) by Bilgi Yılmaz
The Greeks of options are problematic to calculate both numerically and analytically when the str... more The Greeks of options are problematic to calculate both numerically and analytically when the structure of the payoff function of option is complex. This problem can be solved by employing Malliavin calculus. In this study, we summarize the fundamentals of Malliavin Calculus which are useful for computing the sensitivities of options. Then, we use these fundamentals to derive explicit formulas for the Greeks of European and Asian options for the Black-Scholes model and Heston stochastic volatility model. Further, we numerically compute the Greeks of options on ISE and illustrate our results.
Papers by Bilgi Yılmaz
Energy Sources, Part B: Economics, Planning, and Policy, 2022
Efficient electricity demand planning is crucial for energy market actors. However, it is difficu... more Efficient electricity demand planning is crucial for energy market actors. However, it is difficult as a consequence of climate change. We aim at investigating how climate variables (heating and cooling degree days) may affect electricity demand. By examining electricity consumption in various US sectors, we explore this relationship using parametric and non-parametric D-vine quantile regression models that exploits the dependence between covariates and allows sequential covariate selection. The results are compared against the classical linear quantile regression. We find a positive effect of the climatic variables on electricity consumption that is as heating and cooling degree days increase electricity demand rises in all sectors, and cooling need has a greater impact than heating need. Evidence suggests that residential and commercial electricity consumptions are affected the most, while industrial and transport sector consumptions are less sensitive. The D-vine quantile regression performs better than the linear quantile regression for almost all sectors.
Computational economics, Jun 25, 2024
The study focuses on constructing a mathematical housing market threatened by a major catastrophi... more The study focuses on constructing a mathematical housing market threatened by a major catastrophic event or crash. It incorporates the worst-case scenario portfolio optimization problem as introduced in Korn and Wilmott (Int J Theor Appl Finance 5(02):171-187, 2002) into housing markets. The standard stochastic models for housing markets assume a geometric Brownian motion and neglect sudden housing price falls during crash times. However, the size, timing, and frequency of crashes have to be included in such models. By incorporating the worst-case portfolio optimization problem into housing markets, this study introduces a methodology to construct portfolios for large investors that are robust and resilient to extreme housing market conditions. The worst-case portfolio optimization approach can be used in housing markets to incorporate stress scenarios, minimize potential losses, utilize mathematical techniques, and manage housing investment risk effectively. This study provides valuable insights for large investors seeking to construct housing portfolios prioritizing downside protection and minimizing losses in extreme housing market conditions. Utilizing numerical illustrations, it provides insights into portfolio construction, demonstrating the effectiveness of adjusting portfolios to mitigate downside risks during housing market crises. The results highlight dynamic portfolio management's significance in safeguarding wealth when housing prices undergo significant fluctuations.
Expert systems with applications, Sep 1, 2024
Social Science Research Network, 2024
Journal of Computational and Applied Mathematics, 2022
In this paper, a new approach, the Variance Gamma (VG) model, which is used to capture unexpected... more In this paper, a new approach, the Variance Gamma (VG) model, which is used to capture unexpected shocks (e.g., Covid-19) in housing markets, is proposed to contribute to the standard option-based mortgage valuation methods. Based on the VG model, the closed-form solutions are performed for pricing mortgage default and prepayment options. It solves the options pricing equations explicitly and illustrates numerical results for both mortgage default and prepayment options’ prices. Furthermore, the study enables researchers to monitor the default probability of mortgagors. Analyzing the effect of risks on default and prepayment options using simulations shows that the VG model captures the systematic and systemic (idiosyncratic) risks of default and prepayment options prices with closed-form solutions and computes the mortgage default probabilities. Therefore, it allows lenders a more advanced decision process compared to the standard option-based mortgage valuation method.
İzmir İktisat Dergisi
This paper analyzes the effect of macro-economic, financial and commodity market indicators on ho... more This paper analyzes the effect of macro-economic, financial and commodity market indicators on housing markets. We compare the efficiency of the models generated by Generalized Linear Models (GLM) and Multivariate Adaptive Regression Splines (MARS) according to method free measures for estimating the housing market trend. These models are used for the first time to identify the influence of macro-economic indicators on housing markets and the estimation of the trend in housing markets to our best knowledge. The empirical analysis focuses on the US housing market, and the illustration of the proposed models is done through the monthly historical realizations of S\&P/Case-Shiller National Home Price Index (HPI) and the US macro-economic indicators over the period from 1999-January to 2018-June. It contributes to the literature by highlighting the interaction between macro-economic indicators and housing markets and analyzing the mechanism of housing markets. The findings indicate that...
İzmir iktisat dergisi, Jun 30, 2021
This paper analyzes the effect of macroeconomic , financial and commodity market indicators on ho... more This paper analyzes the effect of macroeconomic , financial and commodity market indicators on housing markets. We compare the efficiency of the models generated by Generalized Linear Models (GLM) and Multivariate Adaptive Regression Splines (MARS) according to method free measures for estimating the housing market trend. These models are used for the first time to identify the influence of macroeconomic indicators on housing markets and the estimation of the trend in housing markets to our best knowledge. The empirical analysis focuses on the US housing market, and the illustration of the proposed models is done through the monthly historical realizations of S\&P/Case-Shiller National Home Price Index (HPI) and the US macroeconomic indicators over the period from 1999-January to 2018-June. It contributes to the literature by highlighting the interaction between macroeconomic indicators and housing markets and analyzing the mechanism of housing markets. The findings indicate that the house price trends are estimated with more accuracy and these models capture the joint influence of explanatory variables. Further, the MARS method is shown to outperform GLM compared to the prediction and forecasting power.
Social Science Research Network, Feb 11, 2020
This study explores the hedging coefficients of the financial options to default and to prepay em... more This study explores the hedging coefficients of the financial options to default and to prepay embedded into mortgage contracts based on the change in spot rate, underlying house price and its volatility. In the computations, the finite-dimensional Malliavin calculus is applied since the distribution of both options is unknown and their payoffs are non-differentiable. Naturally, the hedging coefficients are obtained as a product of option's payoff and an independent weight, which permits the user to derive estimations for the hedging coefficients by running a crude Monte Carlo (MC) algorithm. The simulations reveal that the financial options to default and to prepay are both more sensitive to a change in spot rate than a change in underlying house price and its volatility. There are two potential usages of the hedging coefficients: first, they allow the user to determine the effects of spot rate and underlying house price change and its volatility on the default and prepayment options, and second, borrowers and lenders can replicate and hedge their main portfolio by using the balance between these coefficients and the default and prepayment options. Keywords Mortgage default risk • Mortgage prepayment risk • Malliavin calculus • Hedging coefficients • Monte Carlo simulation Bilgi Yilmaz
Sustainable Energy, Grids and Networks
However its popularity has been rising recently, the root of Turkish REITs industry backs to mid-... more However its popularity has been rising recently, the root of Turkish REITs industry backs to mid-1990s. Representing the critical linkage between finance and real estate, the industry has special importance in Turkish financial and real estate sectors. In this study, the performance of REITs return, in Istanbul Stock Exchange for the period 2008-2013, is analyzed by defining its determinants and comparing the efficiency of single index and Fama-French three factor models. There are three main contributions in this study. As the first in Turkish REITs literature, a major contribution of the study is to show differences of the return variability on individual stock returns based on single index and Fama- French models. From a practical contribution perspective, this study may have wider application and provide a tool for critical decision-making in the REITs portfolio management. The study also provides information to the investors who are willing to get benefit from diversification b...
Mathematical Modelling and Numerical Simulation with Applications
Load modeling is crucial in improving energy efficiency and saving energy sources. In the last de... more Load modeling is crucial in improving energy efficiency and saving energy sources. In the last decade, machine learning has become favored and has demonstrated exceptional performance in load modeling. However, their implementation heavily relies on the quality and quantity of available data. Gathering sufficient high-quality data is time-consuming and extremely expensive. Therefore, generative adversarial networks (GANs) have shown their prospect of generating synthetic data, which can solve the data shortage problem. This study proposes GAN-based models (RCGAN, TimeGAN, CWGAN, and RCWGAN) to generate synthetic load data. It focuses on Türkiye's electricity load and generates realistic synthetic load data. The educated synthetic load data can reduce prediction errors in load when combined with recorded data and enhance risk management calculations.
Pressacademia
Purpose- The study has two main purposes. First, it aims to show the efficiency of pure jump proc... more Purpose- The study has two main purposes. First, it aims to show the efficiency of pure jump processes, more specifically Variance Gamma (VG) and Normal Inverse Gaussian models (NIG), in option pricing by comparing with the Black Scholes (BS) option pricing mode. Second, it aims to calibrate the European options written on BIST30 index. Methodology- We introduce an alternative derivation of option pricing formulas under the VG and NIG model assumption. We analyze the VG and NIG models' pricing performance by comparing their pricing result with the classical BS model for the BIST30 index. Our data includes the BIST30 index daily price and European options written on it from 05 May 2018 to 05 May 2020 with a maturity of 90 days. In the given period, the European call options' strike prices range from 1200 to 1650, and the European put options' strike prices range from 1000 to 1400. To compare their efficiency, first, the models are calibrated by minimizing the sum of squar...
Pressacademia
Purpose- This study aims to illustrate the efficiency of pure jump processes, more specifically V... more Purpose- This study aims to illustrate the efficiency of pure jump processes, more specifically Variance Gamma (VG) and Normal Inverse Gaussian models (NIG), in option pricing by comparing with the Black Scholes (BS) option pricing model for emerging markets. Methodology- This study presents an alternative derivation of option pricing formulas for VG and NIG models. Then, it investigates the VG and NIG models' option pricing performance with the help of new derivation by comparing them with the BS option pricing model for emerging markets for an emerging country, Turkey. The data consists of the BIST30 index daily price and European options written on this index extend from 05 May 2018 to 05 May 2020 for given exercise prices with a maturity of 90 days. In this period, the European call options' strike prices range from 1200 to 1650, and the European put options' strike prices range from 1000 to 1400. To compare the models' efficiency, first, we calibrate the models ...
Energy Sources, Part B: Economics, Planning, and Policy
International Journal of Ambient Energy
Uploads
Talks (Selected Conference/Seminar Presentations) by Bilgi Yılmaz
Papers by Bilgi Yılmaz