Modelagem de superfícies de volatilidades para opções pouco líquidas de ações

Resumo

In this paper it is proposed a volatility surface model for less liquid stock options listed on the stock exchange. The model is a mathematical function that transforms the volatility surface of a liquid option of a stock into a volatility surface of a less liquid option of a stock. The model presents high sensitivity in relation to the mathematical function’s parameters employed. Hence, distinct results may be obtained, for example, if the volatility surface of Ibovespa’s or Vale’s options is considered as a possible parameter of the function. In this case, it is also proposed a methodology that allows a decision about the choice of the most appropriate parameters, using a backtest of the differences observed between realized volatility and proposed. The main hypothesis considered in the model is that the calculated difference between the option’s implied volatility and its historical volatility of its underlying is a measure that has a proportion within the same measurements of all specific underlying. This way, if this measurement and the historical volatility of a specific underlying are known, the “implied” volatility of the option of this underlying may be computed. As well as the uncertainty related to the hypothesis described above, there are others related to the selection of parameters in the model and to the illiquidity of the option and its underlying. The impact of these uncertainties will be reflected in the financial result of the option. This way, it is proposed a conservative financial management model based on reserve of financial results as a provision for these uncertainties. In this work, it is presented tests for some options, showing the provisions hypothetically required in terms of vegas of the options for each underlyings.

Ficha do documento

Tipo

Dissertação

Ano

2010

Instituição

Fundação Getulio Vargas

Fonte

Repositório da FGV

Idioma

Português

Acesso

Não informado

Identificador

oai:repositorio.fgv.br:10438/4305

Temas

EconomiaModelagem Econômica

Palavras-chave

Superfície de volatilidadeLiquidez de opções de açõesIncerteza de modeloOpçõesProvisão financeiraCalibragem de superfíciesBacktestSmileEconomiaLiquidez (Economia)Mercado de opções - Avaliação - Modelos matemáticosInvestimentos - Análise