A Term Structure Model with Cyclical Mean Reversion: Pricing and Risk Management

A Term Structure Model with Cyclical Mean Reversion: Pricing and Risk Management

53 Pages · 2013 · 2.07 MB · English

Keywords: Interest rates, term structure, continuous-time model, derivatives pricing, Fourier series. JEL classification: Martınez, Paul MacManus, Pedro Serrano, and attendants at the 4th International Finance and Banking Society. (IFABS) Section 2 introduces the posited model, its main features

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A Term Structure Model with Cyclical Mean Reversion:Pricing and Risk Management Manuel Moreno, Alfonso Novales and Federico Platania October 12, 2013 Abstract This paper introduces a new continuoustime model for the term st ructure of interest rates as suming that the instantaneous interest rate converges to a cyclic longterm level In short, this model incorporates that assumption modelling the mean reversion le vel by a Fourier series Un der this assumption, we compute closedform expressions for the values of dierent xed income and interest rate derivatives and for relevant risk management me asures Finally, we analyze the empirical in and outofsample performance of our model versus two alternative competitors, namely, those proposed in Vasicek (1977) and Nelson and Siegel (19 87) Our ndings show that this model outperforms both benchmarks Keywords: Interest rates, term structure, continuoustime model, de rivatives pricing, Fourier series JEL classication: C31, C51, G12, G13 Corresponding author: Federico Platania The authors grat efully acknowledge comments from Antonio D´az, Maite Mart´nez, Paul MacManus, Pedro Serrano, and attendants at the 4th International Finance and Banking Society (IFABS) (Valencia, Spain), 18th Annual Conference of the Mu ltinational Finance Society (Rome, Italy), II World Finance Conference (Rhodes, Greece), 9th INFINITI Confere nce on International Finance (Dublin, Ireland), XVIII Finance Forum of the Spanish Finance Association (Elche, Sp ain), and VIII Workshop in Banking and Quantitative Finance (Bilbao, Spain) Manuel Moreno is from University o f Castilla LaMancha, Department of Economic Analysis and Finance, Cobertizo San Pedro M´artir s/n, 45071 Toledo, Spain Email: [email protected] Alfonso Novales Cinca is from Universidad Complutense de Madrid, Departmen t of Quantitative Economics, Madrid, Spain Federico Platania is from Universidad Complutense de Madrid, Depart ment of Quantitative Economics, Madrid, Spain Email: [email protected] Manuel Moreno gratefully a cknowledges nancial support by grants ECO200803058 and JCCM PPII1102900305 Federico Platania gratefully ackn owledges nancial support by FPUMEC grant Alfonso Novales acknowledges nancial support from the Spanish Min istry of Science and Innovation through grant ECO2009 10398 and from Generalitat Valenciana grant PROMETEOII/20 13/015 The usual caveat applies 1 1 Introduction The term structure of interest rates has been thoroughly analyzed in many academic papers and constitutes an issue of special relevance for practitioner s in nancial markets This paper introduces a new continuoustime model for the term structure of intere st rates where the instantaneous spot rate is assumed to converge to a longterm level that changes over time according to a Fourier series That specication allows us to capture a number of changes in the curvature of the term structure, an attractive feature which is also incorporated in the Nels onSiegel and Svensson models through exponential functions, providing these two models with a go od t to market interest rates Table 1 shows some of the models proposed in the academic lite rature, classied in two categories: endogenous and exogenous Endogenous models assume that ch anges in interest rates are aected by one or more factors and propose a certain stochastic behav ior for the factors Under those assumptions, the current term structure can be derived as an implication from the model Popular examples of onefactor models are Vasicek (1977), Brennan a nd Schwartz (1980), or Coxet al (1985) The downside of these models is the lack of an appropr iate t to observed interest rate data To mitigate this drawback some multifactor models have bee n proposed See, for instance, Brennan and Schwartz (1979), Schaefer and Schwartz (1984), Longsta and Schwartz (1992), Due and Kan (1996), or Chen (1996) In contrast, exogenous models consider the current term str ucture as an input and aim to prevent arbitrage opportunities considering interest rates with d ierent maturities A pioneer work in this area was made by Ho and Lee (1986) who proposed a model consist ent with observed data As this model implies a Gaussian distribution and no mean reversion for interest rates, several papers

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