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Research

Access a repository of research articles related to quantitative finance and mathematical modelling of financial instruments that have been written by Octaplus Financial Analytics team members over time.

1. Measuring Banking Portfolio Losses Under an Integrated Framework of Market and Credit Risk

Authors: Jorge C. Kapotas, Pedro Paulo Schirmer

In this paper we measure the combined effects of interest rate and default losses on banking portfolios. We show that for any desired level of confidence, there is a critical level of banking spreads such that for sufficiently large spreads, interest revenues more than offset the banking losses. We introduce two alternative profit and loss measurement approaches and different banking book portfolios. We demonstrate that the banking spreads risk mitigation property can be effectively used to reduce the integrated economic capital needs for banking portfolios under both loss measurement approaches.

December 4, 2015
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2. Emerging Correlations: A Comparative Study of Empirical and Regulatory Credit Correlation Structures in the Small and Medium Enterprises (SME) Segment in Brazil

Authors: Jorge C. Kapotas, Gedson O. Santos, Pedro Paulo Schirmer

This paper presents an analysis of the implied empirical correlations extracted from a credit portfolio comprised of small and medium-sized enterprises (SMEs). Empirical correlations are obtained through maximum likelihood estimates derived from Vasicek’s asymptotic one-factor model and are compared to the Basel Committee SME segment regulatory correlations used in the IRB approach. An analysis of the sample correlations behavior as a function of counterparty size and credit quality is also developed. To this end, the credit portfolio was segmented into sub-portfolios, according to credit quality or rating and counterparty size. The results obtained in this work confirm the main evidence presented in similar international studies.

November, 2008
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3. Asset Pricing Theory and Financial Derivatives in Amblyopic Economies: Market Completion by Futures Contracts

Authors: Jorge C. Kapotas

This work aims to consider the problems of theoretical formalization of assets and derivatives pricing models in developing or emerging economies, whose primitive or basic asset markets assets are still in a development process. It is aimed in this work the construction of a theoretical framework for the pricing of fixed income assets and derivatives in economies where basic fixed income assets do not trade liquidly or even do not exist as a generally priced asset class.

June, 2008
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4. Hedge of the Surface Movements of Implicit Volatility of Currency Options

Authors: Tatiana Iwashita, Jorge C. Kapotas, Pedro Paulo Schirmer

This paper aims to determine the primitive risk factors coefficients of the Brazilian currency implied options volatility surface by means of a PCA (Principal Component Analysis) application technique. Using the main components factor loadings, hedging implied volatility strategies for illiquid over-the-counter options are developed.

April, 2005
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5. Pricing and Hedging Brazilian Currency Options

Authors: João Amaro de Matos, Jorge C. Kapotas, Pedro Paulo Schirmer

We consider the impact on the pricing and hedging of Brazilian foreign exchange options due to the direct action of Brazilian monetary authorities. Currency options in Brazil are denominated in terms of the averaged PTAX800 U.S. Dollar / Brazilian Real exchange rate. The computations suggest that Brazilian PTAX800 options are some kind of hybrid instruments behaving like a plain European option at longer expirations and behaving like an Asian option as expiration approaches. The impact of this effect in the pricing and in the hedging of such options is measured as a function of the number of days to expiration.

June 11, 2004
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6. Risk Management of Fixed Income Assets and Derivatives Portfolios

Authors: Mariela Fernández, Jorge C. Kapotas, Pedro Paulo Schirmer

This work presents a quantitative approach to the measurement risk of portfolios with fixed income assets and derivatives. A Monte-Carlo model of primitive risk factors is developed for the fixed Income portfolios forward pricing. Distributions for portfolio values ​​are presented and analyzed.

April, 2004
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7. Are High Frequency IBOVESPA Returns Gaussian ? A Non-Parametric Approach

Autores: Flávio Henn Ferreira, Jorge C. Kapotas, Marcelo M. Taddeo

Smoothing methods applied to non-parametric probability density estimation are presented in the first two sections of this work. In the final section, an application to the IBOVESPA high frequency log-returns probability distribution is presented and analyzed.

Março 11, 2004
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8. Pricing Credit Derivatives in Brazil

Authors: Jorge C. Kapotas, Pedro Paulo Schirmer and Marcelo M. Taddeo

In this work, the main pricing models for defaultable bonds are presented. For this purpose, structural, intensity and rating models are used. Next, a credit derivative (CDS) is defined and its pricing formula is derived. We conclude this article with an application in the Brazilian securities market.

December 10, 2003
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9. Pricing of Volatility Forward Contracts in the Brazilian Market

Authors: Jorge C. Kapotas, Pedro Paulo Schirmer and Sandro M. Manteiga

In this work, we consider the pricing of a class of volatility derivatives, the variance swaps. The fair value of a variance swap is the forward realized variance expected value. This expectation is calculated from an option with a logarithmic pay-off, which in turn is replicated using real market prices. Applications in the Brazilian market are developed in the second part of this article.

November 28, 2003
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10. Fixed-Income Derivatives in Brazil: Hull-White Model

Authors: Leonardo de Almeida, Pedro Paulo Schirmer, Joe Yoshino

With high interest rates and high volatility, and low liquidity, the modelling the Brazilian fixed income market becomes complex. One of the challenges of financial engineering lies in the implementation of models that capture these phenomena. This paper analyzes in detail the implementation of a one-factor Hull-White model for BM&F’s RDI options. The procedure presented allows the endogenous estimation of the parameters of mean reversion and volatility of the model, despite the low liquidity of the IDI options market.

May 6, 2002
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11. Discontinuities and Volatility Regimes in Derivatives Pricing

Authors: Jorge C. Kapotas

Leaps have historically been part of the body of asset pricing dynamics theory since the 1970s. More recently, efforts have been directed towards the development of a theoretical framework dealing with stochastic volatility in derivatives pricing. This work intends to combine and investigate the effects that jumps and stochastic volatility can simultaneously exert on the valuation of options in general, under different scenarios.

May, 2002
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Note: Materials are made available via download for personal consumption. Articles do not necessarily correspond to the latest published version. Octaplus Financial Analytics is not responsible, in any way, for the use that may be made of the content of the articles.
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