Extended Libor Market Models with Stochastic Volatility

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Subfields: Finance

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Fast strong approximation Monte Carlo schemes for stochastic volatility models (2006, methodology): “Another approach to integrate (2) whilst preserving positivity is to transform the stochastic differential equation to logarithmic coordinates using Itô’s lemma as suggested by Andersen and Brotherton-Ratcliffe (2001). Applying this to the mean-reverting CEV process leads to”
A LOW-BIAS SIMULATION SCHEME FOR THE SABR STOCHASTIC VOLATILITY MODEL (2012, methodology): “Whereas the log-Euler scheme preserves positivity of the asset price process, numerical experiments show that the scheme may become unstable for specific time-step sizes [3].”
COMPLEX LOGARITHMS IN HESTON‐LIKE MODELS (2010, methodology): “Andersen and Brotherton-Ratcliffe [2005], the main reason is of a practical nature.”
A General Stochastic Volatility Model for the Pricing of Interest Rate Derivatives (2009, unknown): “Andersen and Brotherton-Ratciffe (2005) develop a LIBOR market model with unspannned stochastic volatility factors in which the forward rates enter the diffusion terms of the forward rate processes in a flexible way that allows forward rates and their volatilities to be correlated.”
Hermite Polynomial Based Expansion of European Option Prices (2014, unknown): “Similar or related work also includes Hagan and Woodward (1999), Hagan et al. (2002), HenryLabordere (2005), and Andersen and Brotherton-Ratcliffe (2001).”