Pricing the convexity premium of interest rate derivatives indexed to CDI using a HJM multi-factorial model

• Ano de defesa: 2021
• Autor(a) principal: Robinson, Kristopher Krishnamurti Homem de Mello
• Orientador(a): Pinto, Afonso de Campos
• Tipo de documento: Dissertação
• Tipo de acesso: Acesso aberto
• Idioma: eng
• Palavras-chave em Português: Derivativos de taxa de juros; Convexidade; Modelo HJM multi-fatorial
• Palavras-chave em Inglês: Interest rate derivatives; Convexity; HJM multi-factor model
• Link de acesso: https://hdl.handle.net/10438/30992

The stochastic element of the dynamics of interest rates combined with the compounded capitalization of the CDI index generates risks of first and second order on derivatives indexed to a percentage different from 100% of CDI. There is literature focused on this, recurrently brought as reference in this work, however in practice the financial market in a general manner prices correctly the first order risk (delta) without giving such diligent attention to the second order risk (gamma), related to the convexity. Such risk, as it is evidenced throughout this work, is positively related to the volatility of the yield curve, to the difference from 100% CDI to the percentage of CDI that the derivative is indexed, it is also related to the maturity of the derivative, being higher on longer tenor derivatives; altogether with the level of the interest rates yield curve. The current context of low interest rates across the globe, may let agents to dismiss the impact of such second order risks, due to the low level of rates curves, but the lower level of interest rates also led to lengthen the tenors of issued debts and the derivatives associated with such emissions, making the amount of this exposure on longer tenor possibly higher now more than ever. With a potential future normalization of monetary policies taking action on different economies, it is expected that the second order risk related to the convexity of these derivatives appears rapidly then. Therefore, it could be said that it is convenient to address this particular issue now, once again. The aim of this work is to contribute to the literature by analysing the convexity of these derivatives by the robust HJM framework and also by proposing as a tool a polynomial equation that could be used as an estimator of the convexity premium as a function of the percentage of CDI the swap in question is indexed and its maturity; to obtain in a quick manner an educated guess of the value of such convexity, that must be considered when pricing such derivatives. The work is based on historical closing prices of DI futures to estimate the volatility parameters of a multi-factorial HJM model to, with these modeled dynamics, then price through Monte Carlo simulations the premiums associated to the convexity of derivatives indexed to percentages different from 100% of CDI on different maturities.