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Fx with stochastic interest rates
  • Efficient Option Pricing with Multi-Factor Equity-Interest Rate Hybrid Models In this article we discuss multi-factor equity-interest rate hybrid models with a full matrix of correlations. We assume the equity part to be modeled by the Heston model [Heston-1993] with as a short rate process either a Gaussian two-factor model [Brigo,Mercurio-2007] or a stochastic volatility short rate process of Heston type [Heidari, et al.-2007]. We develop an approximation for the discounted characteristic function. Our approximation scheme is based on the observation that sqrt{sigma_t}, with sigma_t a stochastic quantity of CIR type [Cox, et al.-1985], can be well approximated by a normal distribution. Our approximate hybrid fits almost perfectly to the original model in terms of implied Black-Scholes [Black,Scholes-1973] volatilities for European options. Since fast integration techniques allow us to get European style option prices for a whole strip of strikes in a split second, the hybrid approximation can be directly used for model calibration. , L.A.Grzelak, K.Oosterlee, S.Van Weeren (2009)
  • A Hybrid Markov-Functional Model with Simultaneous Calibration to Interest Rate and FX Smile , C.P.Fries (2008)
  • A Multifactoral Cross-Currency LIBOR Market Model With a FX Volatility Skew , W.Benner, L.Zyapkov (2007)
  • The Asymptotic Expansion Formula of Implied Volatility for Dynamic SABR Model and FX Hybrid Model , Y.Osajima (2007)
  • Efficient Calibration to FX Options by Markovian Projection in Cross-Currency LIBOR Market Models , A.Antonov, T.Misirpashaev (2006)
  • An asymptotic FX option formula in the cross currency Libor market model , P.Jaeckel, A.Kawai (2006)
  • A Hybrid Markov-Functional Model with Simultaneous Calibration to Interest Rate and FX Smile In this paper we present a Markov functional hybrid interest rate/fx model which allows the calibration of a given market volatility surface in both dimension simultaneously. We extend the approach introduced in [FriesRott] by introducing a functional for the FX which allows a fast, yet accurate calibration to a given market fx volatility surface. This calibration procedure comes as an additional step to the known calibration of the LIBOR functional. , C.P.Fries, F.Eckstaedt (2006)
  • A Multi-currency Model with FX Volatility Skew , V.Piterbarg (2005)
  • Cross-Currency and Hybrid Markov-Functional Models , C.P.Fries, M.G.Rott (2004)

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