Less-Expensive Pricing and Hedging of Extreme-Maturity Interest Rate Derivatives and Equity Index Options Under the Real-World Measure

This thesis is practically oriented towards the pricing and hedging of long-dated interest rate derivatives and equity index options under Platen’s benchmark approach. It aims to be self-contained for convenience of the reader, including all proofs. Among leading banks and insurance companies there does not appear to exist a generally accepted methodology of accurately pricing and hedging such over-the-counter derivatives. This remains the case, despite significant efforts by academics and market practitioners since the early 1990s. This thesis revisits this problem in the light of empirical evidence in a much wider modelling framework than that provided by the classical risk neutral approach. The models considered in this thesis are specified by stochastic differential equations that describe the real-world dynamics of two market variables, namely the short rate and the volatility of the growth optimal portfolio (GOP). The latter is essentially a diversified equity index. This thesis assesses for these models their ability to generate reasonably accurate prices and hedges of typical interest rate term structure derivatives and equity index options. When the discounted GOP is modelled as a time-transformed squared Bessel process, fair prices differ from classical risk neutral prices, resulting in lower prices and lower values-at-risk of long-dated derivatives. Also, such models reflect well empirical market features, such as leptokurtic returns, the leverage effect and a stochastic, yet stationary, volatility structure of the equity index. The results of this analysis, which are contained in this thesis, have been supplemented by the publications of Fergusson and Platen [2006], Fergusson and Platen [2014a], Fergusson and Platen [2015b], Fergusson [2017a] and Fergusson [2017b] and the research reports of Fergusson and Platen [2013], Fergusson and Platen [2014b] and Fergusson and Platen [2015a]. In addition, as by-products of the work done in this thesis, the following papers have been published: Thompson et al. [2017], Calderin et al. [2017] and the following have been submitted to journals for publication: Fergusson and Platen [2014c], Fergusson and Platen [2017]. Finally, the following working papers are to be submitted to journals shortly: Fergusson [2017c], Fergusson [2017d], Fergusson [2017e].