Publicação
Comparison of Black-Scholes and Heston models
| Resumo: | The goal of this dissertation is to compare the Black-Scholes and the Heston model using Deterministic Volatility Functions (DVF) on option pricing. It is important to emphasize that consistency in the choice of loss functions is crucial. On one hand, for any given model, the loss function should be the same for the parameter estimation and model evaluation, otherwise suboptimal parameter estimates can happen. On the other hand, the estimation of loss functions should be identical across models, in order to avoid inappropriate comparisons. Therefore, it will be used three different loss functions in order to estimate and evaluate which of these option valuation models is the most accurate. The sample data contains S&P 500 Index options traded on Chicago Board Options Exchange (CBOE) and it was considered some exclusionary criteria as suggested by Dumas et al. (1998). The remaining data needed to price options was the risk-free rate for each option maturity and the S&P 500 estimated dividend-yield. For both models, the practical application starts with the usage of the Ordinary Least Squares (OLS), with the objective to minimize the Implied Volatility Root Mean Squared Error for each DVF. Secondly, the objective was to minimize the Dollar Root Mean Squared Error and the Percentage Root Mean Squared Error using the Non-linear Least Squares (NLS), for each DVF. For the Heston model, the parameters are estimated using the loss functions, to get the quoted option prices as close to the model option values as possible. After estimating the loss functions, the objective is to decide which model is the most accurate for option pricing. |
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| Autores principais: | Soares, João Pedro Rodrigues |
| Assunto: | Black-Scholes Heston Loss functions Volatilidade -- Volatility |
| Ano: | 2023 |
| País: | Portugal |
| Tipo de documento: | dissertação de mestrado |
| Tipo de acesso: | acesso aberto |
| Instituição associada: | ISCTE |
| Idioma: | inglês |
| Origem: | Repositório ISCTE |
| Resumo: | The goal of this dissertation is to compare the Black-Scholes and the Heston model using Deterministic Volatility Functions (DVF) on option pricing. It is important to emphasize that consistency in the choice of loss functions is crucial. On one hand, for any given model, the loss function should be the same for the parameter estimation and model evaluation, otherwise suboptimal parameter estimates can happen. On the other hand, the estimation of loss functions should be identical across models, in order to avoid inappropriate comparisons. Therefore, it will be used three different loss functions in order to estimate and evaluate which of these option valuation models is the most accurate. The sample data contains S&P 500 Index options traded on Chicago Board Options Exchange (CBOE) and it was considered some exclusionary criteria as suggested by Dumas et al. (1998). The remaining data needed to price options was the risk-free rate for each option maturity and the S&P 500 estimated dividend-yield. For both models, the practical application starts with the usage of the Ordinary Least Squares (OLS), with the objective to minimize the Implied Volatility Root Mean Squared Error for each DVF. Secondly, the objective was to minimize the Dollar Root Mean Squared Error and the Percentage Root Mean Squared Error using the Non-linear Least Squares (NLS), for each DVF. For the Heston model, the parameters are estimated using the loss functions, to get the quoted option prices as close to the model option values as possible. After estimating the loss functions, the objective is to decide which model is the most accurate for option pricing. |
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