Now the arena of interest rate derivatives has its own APT: the Andersen-Piterbarg Textbook.Peter Carr, Global Head of Market Modeling, Morgan Stanley This is a most comprehensive book on interest rate modeling and derivatives valuation. , ), the proof for this statement is given when a single yield curve is considered.Piterbarg Type: eBook Released: 2010 Publisher: Atlantic Financial Press Page Count: 376 Format: djvu Language: English ISBN-10: ISBN-13: 111 Review In the seventies, Arbitrage Pricing Theory (APT) was invented for equity derivatives. An equity-interest rate hybrid model with stochastic volatility and interest rate smile, the Netherlands: Submitted for publication, Technical Report 10-01, SSRN Working Paper, Delft University Technology. ģ The model parameters do not satisfy the Feller condition,Ĥ As it is insightful to relate the covariance matrix with the necessary model approximations, the correlation structure is introduced here by means of instantaneous correlation of the scalar diffusions.ĥ In Grzelak and Oosterlee ( 2010 Grzelak, L. ,, ) the n-dimensional system of SDEs, is of the affline form if for i, j = 1,…, n, with r( X(t)) being an interest rate component.Ģ Since the moments of the square root process under the T-forward measure are difficult to determine for, we have set or, in other words, the expectation is calculated under measure. Transform analysis and asset pricing for affine jump-diffusions. Finally, we add a correlated stock to the framework and discuss the construction, model calibration and pricing of equity–FX–interest rate hybrid pay-offs.ġ According to Duffie et al. We provide semi-closed form approximations which lead to efficient calibration of the multi-currency models. 1–32), which can model an interest rate smile. Volatility skews and extensions of the libor market model, Applied Mathematics Finance, 1, pp. We then extend the framework by modelling the interest rate by an SV displaced-diffusion (DD) Libor Market Model (Andersen, L. Pricing interest-rate derivative securities, Review of Financial Studies, 3, pp. We first deal with a foreign exchange (FX) model of Heston-type, in which the domestic and foreign interest rates are generated by the short-rate process of Hull–White (Hull, J. We construct multi-currency models with stochastic volatility (SV) and correlated stochastic interest rates with a full matrix of correlations.
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