Theory and Calibration of Swap Market Models

Galluccio, Stefano; Ly, J.-M.; Huang, Zhijiang; Scaillet, Olivier

doi:10.1111/j.1467-9965.2007.00296.x

Cited by 31 publications

(30 citation statements)

References 39 publications

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“…When considering, at each tenor date, whether or not to exercise the option to enter into a swap contract, the holder needs to consider the forward swap rate dynamics from that tenor date until final maturity. The advantage of co-terminal SMM over other market models in pricing Bermudan swaptions has already been noted and discussed in Jamshidian (1997) [34] and Galluccio, Huang, Ly and Scaillet (2007) [20]. Furthermore, Galluccio, Huang, Ly and Scaillet (2007) [20] use graph theory to classify the "admissible" market models into co-initial, co-sliding and co-terminal subgroups.…”

Section: The Swap Market Modelmentioning

confidence: 99%

“…The advantage of co-terminal SMM over other market models in pricing Bermudan swaptions has already been noted and discussed in Jamshidian (1997) [34] and Galluccio, Huang, Ly and Scaillet (2007) [20]. Furthermore, Galluccio, Huang, Ly and Scaillet (2007) [20] use graph theory to classify the "admissible" market models into co-initial, co-sliding and co-terminal subgroups. They show that the LMM is the only admissible model for swaps of a co-sliding type.…”

Section: The Swap Market Modelmentioning

confidence: 99%

“…In Galluccio et al (2007) [20], the co-terminal SMM is defined by introducing a collection of mutually equivalent probability measures and a family of Brownian motions such that all forward swap rates satisfy the…”

Section: The Swap Market Modelmentioning

confidence: 99%

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Choice of Interest Rate Term Structure Models for Assets and Liability Management

et al. 2008

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The working papers are produced by The University of Manchester -Manchester Business School and are to be circulated for discussion purposes only. Their contents should be considered to be preliminary. The papers are expected to be published in due course, in a revised form and should not be quoted without the authors' permission. Author(s) and affiliation AbstractThis paper compares the pricing and hedging performance of the LMM model against two spot-rate models, namely Hull-White and Black-Karasinski, and the more recent Swap Market Model from an Asset-Liability-Management (ALM) perspective. In contrast to previous studies in the literature, our emphasis here is on ALM and we use hedging performance on Bermudan swaptions to proxy risk management outcome of long-term mortgage loans. Our tests involve calibrating the four interest rate models to European swaption prices for EURO and USD over the period February 2005 to September 2007. The calibrated models are then used to price and hedge a constant 11-year Bermudan swaption portfolio using a series of interest rate swaps and a 1-year holding-revision period. Our empirical results show that, the calibrated parameters of all four models are stable and their pricing errors are small and comparable. No single model dominates in the pricing exercise. The hedging performance of all four models is similar for the Euro market. For the USD market, the short rate models perform marginally better than SMM and LMM. The HW model is marginally better than BK model in terms of model parameter stability and smaller pricing and hedging errors. The hedging performance of all four models is similar for the Euro market. For the USD market, the short rate models perform marginally better than SMM and LMM. The HW model is marginally better than BK model in terms of model parameter stability and smaller pricing and hedging errors. How to quote or cite this document

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Section: The Swap Market Modelmentioning

confidence: 99%

Section: The Swap Market Modelmentioning

confidence: 99%

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Choice of Interest Rate Term Structure Models for Assets and Liability Management

et al. 2008

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“…Then the strike rate and the time T 0 forward swap rate can be derived by equation (4). to improve the computational e¢ ciency, we need to set initial values and boundaries for these parameters.…”

Section: Calibration Of Co-terminal Smmmentioning

confidence: 99%

Swap Market Model: Theory and Empirical Evidence

Poon¹,

Gan

Guan³

2008

SSRN Journal

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Standard-Nutzungsbedingungen:Die Dokumente auf EconStor dürfen zu eigenen wissenschaftlichen Zwecken und zum Privatgebrauch gespeichert und kopiert werden.Sie dürfen die Dokumente nicht für öffentliche oder kommerzielle Zwecke vervielfältigen, öffentlich ausstellen, öffentlich zugänglich machen, vertreiben oder anderweitig nutzen.Sofern die Verfasser die Dokumente unter Open-Content-Lizenzen (insbesondere CC-Lizenzen) zur Verfügung gestellt haben sollten, gelten abweichend von diesen Nutzungsbedingungen die in der dort genannten Lizenz gewährten Nutzungsrechte. The working papers are produced by The University of Manchester -Manchester Business School and are to be circulated for discussion purposes only. Their contents should be considered to be preliminary. The papers are expected to be published in due course, in a revised form and should not be quoted without the authors' permission. Terms of use: Documents in Author(s) and affiliation AbstractThis paper tests the co-terminal swap market model (SMM) pricing and hedging performance on Bermudan swaptions. To our knowledge, the drift for SMM is derived explicitly for the first time here, and the procedures for calibration and simulation using a collection of forward swap rates are also shown in detail. The Longstaff-Schwartz least square method is used to approximate the early exercise decision in Bermudan swaption. By introducing individual parameters for volatility of each co-terminal forward swap rate, the model can match the market quoted European swaption price perfectly. It is noted that, for the SMM, one particular volatility formula may not be enough to capture the term structure of different markets. Hedging performance of the model is tested on Euro and USD European co-terminal swaption using a set of swaps as hedge instrument. Principle component analysis (PCA) is adopted to capture the trend of the forward rates' movement and absolute mean of the PCA factors is used for the bumping of forward rate curve. Hedge ratio is calculated based on the delta ratios with respect to PCA factors. P&L of the hedge portfolio generated by co-terminal SMM is examined on Euro and USD market. The result shows that more factors may be needed in order to improve the hedge performance of the model. Nevertheless, the SMM is very similar to LMM in terms of implementation and model performance, and the SMM is more convenient when dealing with exotic interest rate derivatives where swap rate is the underlying. on Bermudan swaptions. To our knowledge, the drift for SMM is derived explicitly for the first time here, and the procedures for calibration and simulation using a collection of forward swap rates are also shown in detail. The Longstaff-Schwartz least square method is used to approximate the early exercise decision in Bermudan swaption. By introducing individual parameters for volatility of each co-terminal forward swap rate, the model can match the market quoted European swaption price perfectly. It is noted that, for the SMM, one particular volatility formula may no...

show abstract

“…The rates evolved are typically LIBOR rates or swaprates and one then has automatic calibration not just to the value of the rate but also to options on that rate; that is caplets and swaptions. The original cases studied were contiguous LIBOR rates and co-terminal swap rates, (Brace et al, 1997, Jamshidian, 1997 however, more general cases have recently been examined also, (Gallucio et al 2007, Gallucio and Hunter 2004, Pietersz and Regenmortel 2006, including the concept of a generic market model. For detailed accounts of market models, see Brigo and Mercurio (2001), or Musiela and Rutkowski (1997).…”

Section: Introductionmentioning

confidence: 99%