Multiple stochastic volatility extension of the Libor market model and its implementation

In this paper we propose an extension of the Libor market model with a highdimensional specially structured system of square root volatility processes, and give a road map for its calibration. As such the model is well suited for Monte Carlo simulation of derivative interest rate instruments. As a key issue, we require that the local covariance structure of the market model is preserved in the stochastic volatility extension. In a case study we demonstrate that the extended Libor model allows for stable calibration to the cap-strike matrix. The calibration algorithm is FFT based, so fast and easy to implement

Interest rate models with Markov chains

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A Market Model of Interest Rates with Dynamic Basis Spreads in the presence of Collateral and Multiple Currencies

The recent financial crisis caused dramatic widening and elevated volatilities among basis spreads in cross currency as well as domestic interest rate markets. Furthermore, the wide spread use of cash collateral, especially in fixed income contracts, has made the effective funding cost of financial institutions for the trades significantly different from the Libor of the corresponding payment currency. Because of these market developments, the text-book style application of a market model of interest rates has now become inappropriate for financial firms; It cannot even reflect the exposures to these basis spreads in pricing, to say nothing of proper delta and vega (or kappa) hedges against their movements. This paper presents a new framework of the market model to address all these issues.

The least squares method for option pricing revisited

It is shown that the the popular least squares method of option pricing converges even under very general assumptions. This substantially increases the freedom of creating different implementations of the method, with varying levels of computational complexity and flexible approach to regression. It is also argued that in many practical applications even modest non-linear extensions of standard regression may produce satisfactory results. This claim is illustrated with examples

A flexible matrix Libor model with smiles

We present a flexible approach for the valuation of interest rate derivatives based on Affine Processes. We extend the methodology proposed in Keller-Ressel et al. (2009) by changing the choice of the state space. We provide semi-closed-form solutions for the pricing of caps and floors. We then show that it is possible to price swaptions in a multifactor setting with a good degree of analytical tractability. This is done via the Edgeworth expansion approach developed in Collin-Dufresne and Goldstein (2002). A numerical exercise illustrates the flexibility of Wishart Libor model in describing the movements of the implied volatility surface

Consistent Re-Calibration of the Discrete-Time Multifactor Vasi\v{c}ek Model

The discrete-time multifactor Vasi\v{c}ek model is a tractable Gaussian spot rate model. Typically, two- or three-factor versions allow one to capture the dependence structure between yields with different times to maturity in an appropriate way. In practice, re-calibration of the model to the prevailing market conditions leads to model parameters that change over time. Therefore, the model parameters should be understood as being time-dependent or even stochastic. Following the consistent re-calibration (CRC) approach, we construct models as concatenations of yield curve increments of Hull-White extended multifactor Vasi\v{c}ek models with different parameters. The CRC approach provides attractive tractable models that preserve the no-arbitrage premise. As a numerical example, we fit Swiss interest rates using CRC multifactor Vasi\v{c}ek models.Comment: 29 pages, 16 figures, 2 table

Collateral Posting and Choice of Collateral Currency -Implications for Derivative Pricing and Risk Management-

In recent years, we have observed the dramatic increase of the use of collateral as an important credit risk mitigation tool. It has become even rare to make a contract without collateral agreement among the major financial institutions. In addition to the significant reduction of the counterparty exposure, collateralization has important implications for the pricing of derivatives through the change of effective funding cost. This paper has demonstrated the impact of collateralization on the derivative pricing by constructing the term structure of swap rates based on the actual market data. It has also shown the importance of the ?choice? of collateral currency. Especially, when the contract allows multiple currencies as eligible collateral and free replacement among them, the paper has found that the embedded ?cheapest-to-deliver? option can be quite valuable and significantly change the fair value of a trade. The implications of these findings for market risk management have been also discussed.

"Collateral Posting and Choice of Collateral Currency - Implications for Derivative Pricing and Risk Management-"

In recent years, we have observed the dramatic increase of the use of collateral as an important credit risk mitigation tool. It has become even rare to make a contract without collateral agreement among the major financial institutions. In addition to the significant reduction of the counterparty exposure, collateralization has important implications for the pricing of derivatives through the change of effective funding cost. This paper has demonstrated the impact of collateralization on the derivative pricing by constructing the term structure of swap rates based on the actual market data. It has also shown the importance of the "choice" of collateral currency. Especially, when the contract allows multiple currencies as eligible collateral and free replacement among them, the paper has found that the embedded "cheapest-to-deliver" option can be quite valuable and significantly change the fair value of a trade. The implications of these findings for market risk management have been also discussed.