Title Portuguese:
Pricing Asian interest rate options with a Three-Factor HJM Model
Abstract:
Pricing interest rate derivatives is a challenging task that has attracted the attention of many researchers in recent decades. Portfolio and risk managers, policymakers, traders and more generally all market participants are looking for valuable information from derivative instruments. We use a standard procedure to implement the HJM model and to price IDI options. We intend to assess the importance of the principal components of pricing and interest rate hedging derivatives in Brazil, one of the major emerging markets. Our results indicate that the HJM model consistently underprices IDI options traded in the over-the-counter market while it overprices long-term options traded in the exchange studied. We also find a direct relationship between time to maturity and pricing error and a negative relation with moneyness.
Abstract Portuguese:
O apreçamento de instrumentos derivativos de taxa de juros tem atraído a atenção de muitos pesquisadores. Gerentes de risco, operadores e mais genericamente, todos os participantes do mercado, procuram informações nos derivativos. Neste trabalho, implementamos o modelo HJM para apreçar opções de IDI. O objetivo é demonstrar a importância dos componentes principais da estrutura de taxa de juros no apreçamento e no hedge dos derivativos no mercado brasileiro. Os resultados indicam que o modelo HJM consistentemente subapreça as opções de IDI no mercado de balcão e superapreça as opções de prazo maior negociadas na BM&F. Além disso, observa-se que o erro de apreçamento apresenta uma relação diretamente positiva com o tempo para vencimento e negativa com a proximidade do dinheiro.
ABNT Citation:
BARBEDO, C. H. S.; LION, O. B.; VICENTE, J. V. M. Pricing Asian interest rate options with a Three-Factor HJM Model. Revista Brasileira de Finanças, v. 8, n. 1, art. 90, p. 9-23, 2010.
APA Citation:
Barbedo, C. H. S., Lion, O. B., & Vicente, J. V. M. (2010). Pricing Asian interest rate options with a Three-Factor HJM Model. Revista Brasileira de Finanças, 8(1), 9-23.
Permalink:
https://www.spell.org.br/documentos/ver/4507/pricing-asian-interest-rate-options-with-a-three-factor-hjm-model/i/en
References:
Almeida, C. I. & Vicente, J. V. (2006). The role of fixed income options on the risk assessment of bond portfolios. Working Paper.
Almeida, L. A., Yoshino, J., & Schirmer, P. P. S. (2003). Derivativos de renda fixa no Brasil: Modelo Hull-White. Pesquisa e Planejamento Econômico, 33:299– 333.
Amin, K. I. & Morton, A. J. (1994). Implied volatility functions in arbitrage-free term structure models. Journal of Financial Economics, 35:141–180.
Barbachan, J. S. F. & Ornelas, J. R. H. (2003). Apreçamento de opções de IDI usando o modelo CIR. Estudos Econômicos , 33:287–323.
Barcinski, A. (2000). Hedging strategies using a multifactor model for the Brazilian interest rate. Working Paper.
Black, F. (1976). The pricing of commodity contracts. Journal of Financial Economics, 3:167–179.
Black, F., Derman, E., & Toy, W. (1990). A one-factor model of interest rates and its application to treasury bond options. Financial Analysts Journal, JanuaryFebruary:33–39.
Brigo, D. & Mercurio, F. (2006). Interest Rate Models: Theory and Practice. Springer Verlag.
B¨uhler, W., Uhrig-Homburg, M., Walter, U., & Weber, T. (1999). An empirical comparison of foward-rate and spot-rate models for valuing interest rate options. Journal of Finance, 54:269–305.
Chiarelli, C. & Kwon, O. (2007). Classes of interest rate models under the HJM framework. Working Paper. University of Technology Sydney.
Collin, D. P. & Goldstein, R. S. (2002). Do bonds span the fixed income markets? Theory and evidence for unspanned stochastic volatility. Journal of Finance, 57:1685–1730.
Cox, J. C., Ingersoll, J. E., & Ross, S. A. (1985). A theory of the term structure of interest rates. Econometrica, 53:385–407.
Duffie, D. & Kan, R. (1996). A yield factor model of interest rates. Mathematical Finance, 6:379–406.
Gluckstern, M. C. (2001). Aplicac¸˜ao do modelo de Hull-White `a precificac¸˜ao de opc¸˜oes sobre IDI. Doctoral Thesis in Business Economics – Fundação Getúlio Vargas – SP.
Harrison, M. & Kreps, D. (1979). Martingales and arbitrage in multiperiod security markets. Journal of Economic Theory, 20:381–408.
Harrison, M. & Pliska, S. (1981). Martingales and stochastic integrals in the theory of continuous trading. Stochastic Processes and their Applications, 11:215–260.
Heath, D., Jarrow, R., & Morton, A. (1992). Bond pricing and the term structure of interest rates: A new methodology. Econometrica, 60:77–105.
Heidari, M. & Wu, L. (2003). Are interest rates derivatives spanned by the term structure of interest rates? Journal of Fixed Income, 13:75–86.
Hull, J. & White, A. (1993). One-factor interest-rate models and the valuation of interest-rate derivative securities. Journal of Financial and Quantitative Analysis, 28:235–253.
Junior, A. F., Greco, F., Lauro, C., Francisco, G., Rosenfeld, R., & Oliveira, R. (2003). Application of Hull-White model to Brazilian IDI options. Anais do Encontro da Sociedade Brasileira de Finanças.
Knez, P., Litterman, R., & Scheinkman, J. (1994). Exploration into factors explaining money market returns. Journal of Finance, 1:54–61.
Litterman, R. & Scheinkman, J. (1991). Common factors affecting bond returns. Journal of Fixed Income, 1:54–61.
Luna, F. (2006). Aplicação da metodologia de componentes principais na análise da estrutura a termo de taxa de juros brasileira e no cálculo de valor em risco. Texto para Discussão 1146. Brasília, IPEA.
Ritchken, P. & Sankarasubramanian, L. (1995). Volatility structures of forward rates and the dynamics of the term structure. Mathematical Finance, 5:55–72.
Vasicek, O. (1977). An equilibrium characterization of the term structure. Journal of Financial Economics, 5:177–188.
Vieira Neto, C. A. & Valls Pereira, P. L. (2000). Closed form formula for the arbitrage free price of an option for the one day interfinancial deposits index. Anais do XXI Encontro Brasileiro de Econometria.