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61
The Performance of MultiFactor Term Structure Models for Pricing and Hedging Caps and Swaptions
, 2002
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Arbitragefree discretization of lognormal forward Libor and swap rate models
"... . An important recent development in the pricing of interest rate derivatives is the emergence of models that incorporate lognormal volatilities for forward Libor or forward swap rates while keeping interest rates stable. These market models have three attractive features: they preclude arbitrage am ..."
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. An important recent development in the pricing of interest rate derivatives is the emergence of models that incorporate lognormal volatilities for forward Libor or forward swap rates while keeping interest rates stable. These market models have three attractive features: they preclude arbitrage among bonds, they keep rates positive, and, most distinctively, they price caps or swaptions according to Black's formula, thus allowing automatic calibration to market data. But these features of continuoustime formulations are easily lost when the models are discretized for simulation. We introduce methods for discretizing these models giving particular attention to precluding arbitrage among bonds and to keeping interest rates positive even after discretization. These methods transform the Libor or swap rates to positive martingales, discretize the martingales, and then recover the Libor and swap rates from these discretized variables, rather than discretizing the rates themselves. Choosin...
An Empirical Comparison of ForwardRate and SpotRate Models for Valuing InterestRate Options
 The Journal of Finance
, 1999
"... Our main goal is to investigate the question of which interestrate options valuation models are better suited to support the management of interestrate risk. We use the German market to test seven spotrate and forwardrate models with one and two factors for interestrate warrants for the period ..."
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Our main goal is to investigate the question of which interestrate options valuation models are better suited to support the management of interestrate risk. We use the German market to test seven spotrate and forwardrate models with one and two factors for interestrate warrants for the period from 1990 to 1993. We identify a onefactor forwardrate model and two spotrate models with two factors that are not significantly outperformed by any of the other four models. Further rankings are possible if additional criteria are applied. A VALUATION MODEL FOR INTERESTRATE derivatives represents the core of any system designed to measure, control, and supervise interestrate risk. This is true regardless of whether a valueatrisk methodology, sensitivity analysis, stress test, or scenario technique is applied. Unfortunately, there is no empirical evidence that evaluates the performance of the most popular competing pricing models using the same data from a risk management perspective. This paper provides such empirical evidence using data from the German market for
Reserving, pricing and hedging for policies with guaranteed annuity options. Forthcoming
 in the British Actuarial Journal
, 2003
"... In this paper we consider reserving and pricing methodologies for a pensionstype contract with a simple form of guaranteed annuity option. We consider only unitlinked contracts, but our methodologies and, to some extent, our numerical results would apply also to with profits contracts. The Report ..."
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Cited by 14 (2 self)
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In this paper we consider reserving and pricing methodologies for a pensionstype contract with a simple form of guaranteed annuity option. We consider only unitlinked contracts, but our methodologies and, to some extent, our numerical results would apply also to with profits contracts. The Report of the Annuity Guarantees Working Party, Bolton et al. (1997), presented the results of a very interesting survey as at the end of 1996 of life assurance companies offering guaranteed annuity options. There was no consensus at that time among the companies on how to reserve for such options. The Report discussed several approaches to reserving but concluded that it was unable to recommend a single approach. This paper is an attempt to fill that gap. We investigate two approaches to reserving and pricing. In the first sections of the paper we consider quantile, and conditional tail expectation, reserves. The methodology we adopt here is very close to that proposed by the Maturity Guarantees Working Party in its Report to the profession, Ford et al. (1980). We show how these policies could have been reserved for in 1985, and what would have been the outcome of using the proposed method.
Bootstrapping the Illiquidity: Multiple Yield Curves Construction For Market Coherent Forward Rates Estimation”, to be published in “Modeling Interest Rates: Latest Advances for Derivatives Pricing”, edited by
, 2009
"... Abstract. The large basis spreads observed on the interest rate market since the liquidity crisis of summer 2007 imply that different yield curves are required for market coherent estimation of forward rates with different tenors (e.g. Euribor 3 months, Euribor 6 months, etc.). In this paper we rev ..."
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Abstract. The large basis spreads observed on the interest rate market since the liquidity crisis of summer 2007 imply that different yield curves are required for market coherent estimation of forward rates with different tenors (e.g. Euribor 3 months, Euribor 6 months, etc.). In this paper we review the methodology for bootstrapping multiple interest rate yield curves, each homogeneous in the underlying rate tenor, from nonhomogeneous plain vanilla instruments quoted on the market, such as Deposits, Forward Rate Agreements, Futures, Swaps, and Basis Swaps. The approach includes turn of year effects and is robust to deliver smooth yield curves and to ensure nonnegative rates also in highly stressed market situations, characterized by crazy roller coaster shapes of the market quotations. The concrete EUR market case is analyzed in detail, using the open source QuantLib implementation of the proposed algorithms. 1.
Yield curve shapes and the asymptotic short rate distribution in affine onefactor models
 Finance and Stochastics, 12: 149 – 172
, 2008
"... Abstract. We consider a model for interest rates, where the short rate is given by a timehomogenous, onedimensional affine process in the sense of Duffie, Filipović, and Schachermayer. We show that in such a model yield curves can only be normal, inverse or humped (i.e. endowed with a single local ..."
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Cited by 9 (5 self)
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Abstract. We consider a model for interest rates, where the short rate is given by a timehomogenous, onedimensional affine process in the sense of Duffie, Filipović, and Schachermayer. We show that in such a model yield curves can only be normal, inverse or humped (i.e. endowed with a single local maximum). Each case can be characterized by simple conditions on the present short rate rt. We give conditions under which the short rate process will converge to a limit distribution and describe the limit distribution in terms of its cumulant generating function. We apply our results to the Vasiček model, the CIR model, a CIR model with added jumps and a model of OrnsteinUhlenbeck type. 1.
On the information in the interest rate term structure and option prices’, Review of Derivatives Research
, 2004
"... Cap and swaption prices contain information on interest rate volatilities and correlations. In this paper, we examine whether this information in cap and swaption prices is consistent with realized movements of the interest rate term structure. To extract an optionimplied interest rate covariance m ..."
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Cited by 7 (1 self)
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Cap and swaption prices contain information on interest rate volatilities and correlations. In this paper, we examine whether this information in cap and swaption prices is consistent with realized movements of the interest rate term structure. To extract an optionimplied interest rate covariance matrix from cap and swaption prices, we use Libor market models and discretetenor string models as a modelling framework. We propose a flexible parameterization of the interest rate covariance matrix, which cannot be generated by standard lowfactor term structure models. The empirical analysis is based on weekly US data from 1995 to 1999. Our empirical results show that the option prices imply a covariance matrix of interest rates that is significantly different from the covariance matrix implied by realized interest rate changes. In particular, 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.
Using path integrals to price interest rate derivatives
"... Abstract: We present a new approach for the pricing of interest rate derivatives which allows a direct computation of option premiums without deriving a (BlackScholes type) partial differential equation and without explicitly solving the stochastic process for the underlying variable. The approach ..."
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Abstract: We present a new approach for the pricing of interest rate derivatives which allows a direct computation of option premiums without deriving a (BlackScholes type) partial differential equation and without explicitly solving the stochastic process for the underlying variable. The approach is tested by rederiving the prices of a zero bond and a zero bond option for a short rate environment which is governed by Vasicek dynamics. Furthermore, a generalization of the method to general short rate models is outlined. In the case, where analytical solutions are not accessible, numerical implementations of the path integral method in terms of lattice calculations as well as path integral Monte Carlo simulations are possible. 1 1
B.: LIBOR rate models, related derivatives and model calibration
, 1999
"... Based on Jamshidians framework, [8], a general strategy for the quasianalytical valuation of large classes of LIBOR derivatives will be developed. As a special case we will address the quasianalytical approximation formula for swaptions of Brace Gatarek and Musiela in [2] and show that a similar f ..."
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Cited by 5 (2 self)
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Based on Jamshidians framework, [8], a general strategy for the quasianalytical valuation of large classes of LIBOR derivatives will be developed. As a special case we will address the quasianalytical approximation formula for swaptions of Brace Gatarek and Musiela in [2] and show that a similar formula can be derived with Jamshidian's methods as well. As further applications we will study the callable reverse oater and the trigger swap. Then, we will study the thorny issues around simultaneous calibration of (low factor) LIBOR models to cap(let) and swaption prices in the markets. We will argue that a low factor market model cannot be calibrated to these prices in a stable way and propose an, in fact, many factor model with only the same number of loading parameters as a two factor model, but, with much better stability properties.