Calibrating the LIBOR market model to swaptions with an extension for illiquidity in South Africa

The popularity of the LIBOR Market Model (LMM) in interest rate modelling is a result of its consistency with market practice of pricing interest rate derivatives. In the context of a life insurance company, the LMM is calibrated to swaptions as they are actively traded for a wide variety of maturities and they serve as the natural hedge instruments for many of the long dated maturity products with embedded options. Before calibrating the model we extend the calibration process to address the issue of illiquidity in the South African swaption market. The swaption surface used in calibrating the model is generated with market implied quotes for the hedgeable component and thereafter using historical volatilities for the unhedgeable or illiquid component. Rebonato's 3 parameter correlation function proposed by Rebonato (2005) provides the best fit to historical data. We assume a general piecewise constant parameterisation for the instantaneous forward rate volatilities. These volatilities are then determined analytically using the Rectangular Cascade Calibration Algorithm from Brigo and Morini (2006). The calibration generates a stable volatility term structure with the instantaneous forward rate volatilities being positive and real. Through an extension of the calibration we are able to capture the benefits of a pure replication component and accommodate a large unhedgeable component in the price faced by life insurance companies in South Africa

Applications of Eigensystem Analysis to Derivatives and Portfolio Management

Eigensystem structure plays the key role in principal component analysis (PCA). However, the application of it in high-frequency datasets is noticeably thin, especially for derivatives pricing. In my thesis, I will present the predictive power of eigenvalue/eigenvector analysis in several nancial markets. Performance of prediction based on eigenvalue/eigenvector structure shows the result that this methodology is reliable compared with traditional methodology. To verify the performance of eigensystem analysis in derivatives pricing, I select one of the most important nancial markets: the foreign exchange(FX) option market as datasets. The traditional pricing models for FX options are highly reliant on historical data, which leads to the dilemma that for those contracts with less liquidity investors nd it dicult to provide reliable guidance on price. I will present a brand-new model based on eigensystem analysis to provide accurate guidance for option pricing, especially in cases where the underlying asset is considered to be an illiquid currency pair. The importance of eigenvalues and eigenvectors structure in asset pricing will be explored in this thesis. The empirical study covers FX option contracts across deltas and maturities. The performance of eigensystem model are compared with other widely used models, results indicate that traditional models are outperformed in all selected underlying assets, maturities and deltas. In addition, I perform analysis of machine learning performance based on theFX market's empirical asset pricing problem. I demonstrate the advantage of machine learning in promoting the predictive power of eigensystem based on multiple predictors from the OTC market. Black-Scholes implied volatility is used as predictors for the eigenvalue error between market and our innovative eigensystem. I identify the regression tree algorithm's predictive gain with empirical study across contracts. The eect of currency pairs is numerical and sorted to generate an overview for global FX market structure. I also implement eigenstructure analysis based on the S&P500 market. I discover the convergence of rst principal component explanatory power. In order to generate the statistical summary for trend of principal components, I raise a set of measurements and thresholds to describe eigenvalue and eigenvector structure in market portfolios

The History of the Quantitative Methods in Finance Conference Series. 1992-2007

This report charts the history of the Quantitative Methods in Finance (QMF) conference from its beginning in 1993 to the 15th conference in 2007. It lists alphabetically the 1037 speakers who presented at all 15 conferences and the titles of their papers.

Hybrid multi-curve models with stochastic basis

The financial markets have changed radically since the start of the 2007 credit crisis. Following the bankruptcies of large financial institutions as well as bailouts of multiple banks and asset management institutions like Bear Sterns, Lehman Brothers, and AIG, the market participants recognised the serious credit and liquidity risks present in the widely traded interest rate derivatives. The effect of rising credit and liquidity risks was observed by the spike in the spreads between nearly risk-free OIS rates used for collateral and risky unsecured LIBOR loan rates. Most of the classical interest rate models used by mentioned market participants relied on the assumption that there exists a risk-free and unique LIBOR lending rate, which is no longer true. This has opened new ground for complex, hybrid models for interest rate derivatives. This PhD thesis presents my work on developing novel interest rate models which are mathematically and historically sound and can be used for pricing interest rate derivatives including stochastic basis spreads between unsecured LIBOR and OIS rates. This work is split into two problems: first we analyse the discrepancies between forward-LIBOR lending rates and their classic replication strategy with spot-LIBOR rates. For this problem, we propose an extension of a known LIBOR Panel Model, which enables us to jointly model OIS and spot- and forward-LIBOR rates with an error within the quoted bid-ask spreads. The second part of this thesis looks into the problem of pricing non-linear derivatives like caps linked to rates on multiple LIBOR tenors. We propose a novel hybrid credit-interest rate model, which allows to jointly model OIS and multi-tenor LIBOR rates and to price multi-tenor caps. The proposed hybrid short-rate model is intuitive, semi-analytically tractable and can be calibrated using liquid, available market data. We compare the market data fit with a benchmark model using fixed LIBOR-OIS spread assumption. The last chapter shows the impact of this model on credit value adjustments for interest rate trades

Portfolio advice of a multifactor world

How does traditional portfolio theory adapt to the new facts? The old "two-fund" theorem becomes a "many-fund" theorem; some investors can improve returns by investing in portfolio strategies that let them take on nonmarket sources of risk; and other investors can shed nonmarket risks in the same way. Investors can, if willing to take on risks, improve returns by some modest market timing. However, the average investor must always hold the market, so only investors who are different from average can benefit from holding new and unusual portfoliosMutual funds ; Capital assets pricing model

The Basel III framework for liquidity standards and monetary policy implementation

Basel III introduces for the first time an international framework for liquidity risk regulation, reflecting the experience of excessive liquidity risk taking of banks in the run up to the financial crisis that erupted in August 2007, and associated negative externalities. As central banks play a crucial role in the liquidity provision to banks during normal times and in a financial crisis, the treatment of central bank operations in the regulation is obviously important. To ensure internalisation of liquidity risks (i.e. pricing of liquidity risk) and to address excessive reliance ex ante on central bank liquidity support by the banks, the regulation deliberately does not establish a direct close link with the monetary policy operational framework. While this reflects the purpose of the regulation and is also natural outcome of an international rule being applied under a multitude of very different monetary policy operational frameworks, this paper shows that the interaction between the two areas can be substantial, depending on the operational and collateral framework of the central bank. This implies the need for further study and the development of policies at the central bank and regulatory/supervisory side on how to handle these potential interactions in practice.Basle III, Liquidity Risk, Banking Regulation, monetary policy implementation

A non-arbitrage liquidity model with observable parameters for derivatives

We develop a parameterised model for liquidity effects arising from the trading in an asset. Liquidity is defined via a combination of a trader's individual transaction cost and a price slippage impact, which is felt by all market participants. The chosen definition allows liquidity to be observable in a centralised order-book of an asset as is usually provided in most non-specialist exchanges. The discrete-time version of the model is based on the CRR binomial tree and in the appropriate continuous-time limits we derive various nonlinear partial differential equations. Both versions can be directly applied to the pricing and hedging of options; the nonlinear nature of liquidity leads to natural bid-ask spreads that are based on the liquidity of the market for the underlying and the existence of (super-)replication strategies. We test and calibrate our model set-up empirically with high-frequency data of German blue chips and discuss further extensions to the model, including stochastic liquidity

The aporetic financialisation of insurance liabilities: Reserving under Solvency II

The valuation of insurance liabilities has traditionally been dealt with by actuaries, who closely monitored underlying illiquid features, assumed a long-term perspective, and exercised their own subjective, expert judgment. However, the new EU regulatory regime of Solvency II (S2) has come to require market-consistent valuation supplemented by a risk-sensitive capital. This is considered an unwanted shift towards short-termism that is misaligned with the industry’s long term and countercyclical character. The new principles place the ‘technicalising’ logic of financial economics over ‘contextualising’ actuarial know-how. Following existing analytics of valuation from the ethnography of reinsurance markets and the social studies of finance, such requirements appear either as an alarming attack against the actuarial component of traditional valuation practice, or else as a preserver of it, through a process of enfolding at the heart of the financialisation project. This article holds that the case of S2 challenges both these analytics of valuation. S2’s financialisation project, precisely by attempting to construct itself, deconstructs itself into an actuarial project, in a recurring, aporetic process. In this respect, fair (or otherwise) valuation remains always undecidable, inconclusive, and thus responsible