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1.
We empirically compare Libor and Swap Market Models for thepricing of interest rate derivatives, using panel data on pricesof US caplets and swaptions. A Libor Market Model can directlybe calibrated to observed prices of caplets, whereas a SwapMarket Model is calibrated to a certain set of swaption prices.For both models we analyze how well they price caplets and swaptionsthat were not used for calibration. We show that the Libor MarketModel in general leads to better prediction of derivative pricesthat were not used for calibration than the Swap Market Model.Also, we find that Market Models with a declining volatilityfunction give much better pricing results than a specificationwith a constant volatility function. Finally, we find that modelsthat arechosen to exactly match certain derivative prices areoverfitted; more parsimonious models lead to better predictionsfor derivative prices that were not used for calibration. JELClassification: G12, G13, E43.  相似文献   

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We consider the problem of valuation of interest rate derivatives in the post-crisis set-up. We develop a multiple-curve model, set in the HJM framework and driven by a Lévy process. We proceed with joint calibration to OTM swaptions and co-terminal ATM swaptions of different tenors, the calibration to OTM swaptions guaranteeing that the model correctly captures volatility smile effects and the calibration to co-terminal ATM swaptions ensuring an appropriate term structure of the volatility in the model. To account for counterparty risk and funding issues, we use the calibrated multiple-curve model as an underlying model for CVA computation. We follow a reduced-form methodology through which the problem of pricing the counterparty risk and funding costs can be reduced to a pre-default Markovian BSDE, or an equivalent semi-linear PDE. As an illustration, we study the case of a basis swap and a related swaption, for which we compute the counterparty risk and funding adjustments.  相似文献   

4.
We apply Stroock and Varadhan’s support theorem to show that there is a positive probability that within the Swap Market Model the implied Libor rates become negative in finite time. Mataix-Pastor received support from the Instituto Credito Oficial (ICO), Spain, and Fundación Caja Madrid.  相似文献   

5.
We present a neural network-based calibration method that performs the calibration task within a few milliseconds for the full implied volatility surface. The framework is consistently applicable throughout a range of volatility models—including second-generation stochastic volatility models and the rough volatility family—and a range of derivative contracts. Neural networks in this work are used in an off-line approximation of complex pricing functions, which are difficult to represent or time-consuming to evaluate by other means. The form in which information from available data is extracted and used influences network performance: The grid-based algorithm used for calibration is inspired by representing the implied volatility and option prices as a collection of pixels. We highlight how this perspective opens new horizons for quantitative modelling. The calibration bottleneck posed by a slow pricing of derivative contracts is lifted, and stochastic volatility models (classical and rough) can be handled in great generality as the framework also allows taking the forward variance curve as an input. We demonstrate the calibration performance both on simulated and historical data, on different derivative contracts and on a number of example models of increasing complexity, and also showcase some of the potentials of this approach towards model recognition. The algorithm and examples are provided in the Github repository GitHub: NN-StochVol-Calibrations.  相似文献   

6.
One-factor Markov models are widely used by practitioners for pricing financial options. Their simplicity facilitates their calibration to the intial conditions and permits fast computer Implementations. Nevertheless, the danger remains that such models behave unrealistically, if the calibration of the volatility is not properly done. Here, we study a lognormal process and investigate how to specify the volatility constraints in such a way that the term structure of volatility at future times, as implied by the short rate process, has a realistic and stable shape. However, the drifting down of the volatility term structure is unavoidable. As a result, there is a tendency to underestimate option prices.  相似文献   

7.
We analyze the role of federal funds rate volatility in affecting risk premium as measured by various money market spreads during the 2007–2009 financial crisis. We find that volatility in the federal funds market contributed to elevated Overnight Index Swap (OIS) spreads of unsecured bank funding rates during the crisis. Using OIS as a proxy for market expectations, we also decompose London Inter-Bank Offered Rate (Libor) into its permanent and transitory components in a dynamic factor framework and show that increased volatility in the federal funds market contributed to substantial transitory movements of Libor away from its long-run trend during the financial crisis.  相似文献   

8.
In this paper, we introduce an extension to the LIBOR Market Model (LMM) that is suitable to incorporate both sudden market shocks as well as changes in the overall economic climate into the interest rate dynamics. This is achieved by substituting the simple diffusion process of the original LMM by a regime-switching jump diffusion. We demonstrate that the new Markov-switching jump diffusion (MSJD) LMM can be embedded into a generalized regime-switching Heath–Jarrow–Morton model and prove that the considered market is arbitrage-free. We derive pricing formulas for caps, floors and swaptions using Fourier pricing techniques and show how the model can be calibrated to real market data.  相似文献   

9.
We examine whether the information in cap and swaption prices is consistent with realized movements of the interest rate term structure. To extract an option-implied interest rate covariance matrix from cap and swaption prices, we use Libor market models as a modelling framework. We propose a flexible parameterization of the interest rate covariance matrix, which cannot be generated by standard low-factor term structure models. The empirical analysis, based on US data from 1995 to 1999, shows that option prices imply an interest rate covariance matrix that is significantly different from the covariance matrix estimated from interest rate data. If one uses the latter covariance matrix to price caps and swaptions, one significantly underprices these options. We discuss and analyze several explanations for our findings.  相似文献   

10.
We propose a novel time-changed Lévy LIBOR (London Interbank Offered Rate) market model for jointly pricing of caps and swaptions. The time changes are split into three components. The first component allows matching the volatility term structure, the second generates stochastic volatility, and the third accommodates for stochastic skew. The parsimonious model is flexible enough to accommodate the behavior of both caps and swaptions. For the joint estimation we use a comprehensive data set spanning the financial crisis of 2007–2010. We find that, even during this period, neither market is as fragmented as suggested by the previous literature.  相似文献   

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