Kenneth McKay - Böcker

This book presents a major innovation in the interest rate space. It explains a financially motivated extension of the LIBOR Market model which accurately reproduces the prices for plain vanilla hedging instruments (swaptions and caplets) of all strikes and maturities produced by the SABR model. The authors show how to accurately recover the whole of the SABR smile surface using their extension of the LIBOR market model. This is not just a new model, this is a new way of option pricing that takes into account the need to calibrate as accurately as possible to the plain vanilla reference hedging instruments and the need to obtain prices and hedges in reasonable time whilst reproducing a realistic future evolution of the smile surface. It removes the hard choice between accuracy and time because the framework that the authors provide reproduces today's market prices of plain vanilla options almost exactly and simultaneously gives a reasonable future evolution for the smile surface. The authors take the SABR model as the starting point for their extension of the LMM because it is a good model for European options. The problem, however with SABR is that it treats each European option in isolation and the processes for the various underlyings (forward and swap rates) do not talk to each other so it isn't obvious how to relate these processes into the dynamics of the whole yield curve. With this new model, the authors bring the dynamics of the various forward rates and stochastic volatilities under a single umbrella. To ensure the absence of arbitrage they derive drift adjustments to be applied to both the forward rates and their volatilities. When this is completed, complex derivatives that depend on the joint realisation of all relevant forward rates can now be priced. ContentsTHE THEORETICAL SET-UPThe Libor Market modelThe SABR ModelThe LMM-SABR Model IMPLEMENTATION AND CALIBRATIONCalibrating the LMM-SABR model to Market Caplet pricesCalibrating the LMM/SABR model to Market Swaption PricesCalibrating the Correlation Structure EMPIRICAL EVIDENCEThe Empirical problemEstimating the volatility of the forward ratesEstimating the correlation structureEstimating the volatility of the volatility HEDGINGHedging the Volatility StructureHedging the Correlation StructureHedging in conditions of market stress

‘Poetry,’ wrote Tennyson ‘is like shot-silk with many glancing colours.’ Taking this statement as a key to Tennyson’s art and meaning, Kenneth McKay explores in detail the maturing poems from Tennyson’s earliest efforts as a boy under his father’s eye at Somersby, through ‘Timbuctoo’ and ‘The Lover’s Tale,’ through the great poems published between 1830 and 1847, to their culmination in ‘In Memoriam,’ that complex, various, and subtle expression of Tennyson’s achieved maturity. Rooted in close analyses of individual poems, Many Glancing Colours becomes a study of the development and character of Tennyson’s liberal artistic imagination.Though closely aligned with Coleridge’s idea of ‘multeity in unity,’ Tennyson’s sense of poetry as shot-silk is different, MacKay suggests, chiefly by its resistance to and subversion of a faith in the efficacy of the rational, ordering consciousness. Tennyson rejected Coleridge’s Germany idealism, recognizing in the words of Arthur Hallam, that ‘Pain is the deepest thing we have in our nature, and union through pain has always seemed more real and more holy than any other.’ With this, he saw, again with Hallam, that ‘the Godhead of the Son has not been a fixed, invariable thing from the beginning: he is more God now than he was once; and will be perfectly united to God hereafter.’From this position, McKay argues, Tennyson wrote his great poems between 1830 and 1850, apprehending reality in a body of work which is distinct in a voice, technique, and imaginative grasp. First in ‘Mariana’ (1830) and then in the major poems which follow, Tennyson projects a world in which meaning and love come only as one submits, beyond any hope for or presumption of knowledge, to suffering and ignorance as the very condition of both vision and life. A poetry of shot-silk, in its intelligence, range, variety, and ambiguity, became Tennyson’s natural instrument, one fundamental to his liberal artistic imagination and a study of which makes for a new understanding of the development and character of the Victorian period generally.