2008 Series
Markov Switching GARCH Diffusion
Carol Alexander and Emese Lazar
2008-01
Abstract: GARCH option pricing models have the advantage of a well-established econometric foundation. However, multiple states need to be introduced as single state GARCH and even Lévy processes are unable to explain the term structure of the moments of financial data. We show that the continuous time version of the Markov switching GARCH(1,1) process is a stochastic model where the volatility follows a switching process. The continuous time switching GARCH model derived in this paper, where the variance process jumps between two or more GARCH volatility states, is able to capture the features of implied volatilities in an intuitive and tractable framework.
Stochastic Local Volatility
Carol Alexander and Leonardo Nogueira
2008-02
Abstract: There are two unique volatility surfaces associated with any arbitrage-free set of standard European option prices, the implied volatility surface and the local volatility surface. Several papers have discussed the stochastic differential equations for implied volatilities that are consistent with these option prices but the static and dynamic no-arbitrage conditions are complex, mainly due to the large (or even infinite) dimensions of the state probability space. These no-arbitrage conditions are also instrument-specific and have been specified for some simple classes of options. However, the problem is easier to resolve when we specify stochastic differential equations for local volatilities instead. And the option prices and hedge ratios that are obtained by making local volatility stochastic are identical to those obtained by making instantaneous volatility or implied volatility stochastic. After proving that there is a one-to-one correspondence between the stochastic implied volatility and stochastic local volatility approaches, we derive a simple dynamic no-arbitrage condition for the stochastic local volatility model that is model-specific. The condition is very easy to check in local volatility models having only a few stochastic parameters.
Dependent jump processes with coupled levy measures
Naoufel El-Bachir
2008-03
Abstract: I present a simple method for the modelling and simulation of dependent positive jump processes through a series representation. Each constituent process is represented by a series whose terms are equal to a transformation of the jump times of a standard Poisson process. The transformations are given by the inverses of the respective marginal Levy tail mass integral functions. The dependence between the various consituent processes is given by a probalistic copula for the inter-arrival times of the various standard Poisson processes.
An Assessment of the Internal Rating Based Approach in Basel II
Dr Simone Varotto
2008-04
Abstract: The new bank capital regulation commonly known as Basel II includes a internal rating based approach (IRB) to measuring credit risk in bank portfolios. The IRB relies on the assumptions that the portfolio is fully diversified and that systematic risk is driven by one common factor. In this work we empirically investigate the impact of these assumptions by comparing the risk measures produced by the IRB with those of a more general credit risk model that allows for multiple systematic risk factors and portfolio concentration. Our tests conducted on a large sample of eurobonds over a ten year period reveal that deviations between the IRB and the general model can be substantial.
Maximum Certain Equivalent Excess Returns and Equivalent Preference Criteria Part I - Theory
Dr Jacques Pezier
2008-05
Abstract: Generalizations of traditional preference criteria such as the Sharpe ratio, the information ratio and the Jensen alpha are obtained by maximizing a certain equivalent excess return (CER) under relevant investment conditions. They are increasing functions of CERs and therefore equivalent criteria. They are consistent with utility theory and are applicable to any investment choice. That is not the case for many other popular preference criteria (e.g., Omega index, Sortino ratio, expected shortfall and so-called ‘coherent' preference criteria). Most are incompatible with expected utility maximization and therefore best avoided.
An analytically tractable time-changed jump-diffusion default intensity model
Naoufel El-Bachir and Damiano Brigo
2008-06
Abstract: We present a stochastic default intensity model where the intensity follows a tractable jump-diffusion process obtained by applying a deterministic change of time to a non mean-reverting square root jump-diffusion process. The model generates higher implied volatilities for default swaptions than mean-reverting versions, consistent with volatility levels observed on the market.
Interest in medieval accounts: Examples from England, 1272-1340
Dr Adrian Bell, Dr Chris Brooks and Dr Tony Moore
2008-07
Abstract: Research into medieval interest rates has been hampered by the diversity ofterms and methods used by historians, creating serious misconceptions in the reporting of medieval interest rates, which have then been taken at face value by later scholars. This has had important repercussions on the wider debate on the credit risk of different forms of medieval governments and the costs of borrowing as a bar to investment. This paper seeks to establish a standardised methodology to accurately calculate interest rates from historical sources, which will provide a firmer foundation for comparisons between regions and periods. It also supports other recent literature suggesting that medieval economic and financial development was more advanced than previously portrayed. The paper is illustrated with case studies drawn from the credit arrangements of the English kings between 1272 and c.1340, and argues that the variations over time in interest rates charged reflect the contemporary notion of credit worthiness as it applied to the medieval English Crown.
Optimal Investment Strategies and Performance Sharing Rules for Pension Schemes with Minimum Guarantee
Johanna Scheller and Dr Jacques Pezier
2008-09
Abstract: There is a potential conflict of interest between a pension fund sponsor and future pensioners when they share unequally in the pension fund performance. Thus when a scheme offers a yearly guaranteed minimum return to pensioners, as is presently the case with German Pensionskassen, the managers cannot afford to invest in risky assets and consequently, pensioners end up with safe but very low expected returns. We examine optimal investment strategies for fund managers under alternative profit sharing rules and seek the rules that are most beneficial to pensioners. We find the current yearly performance sharing rule imposed on Pensionskassen could be tilted in favor of managers without impairing the welfare of pensioners. We also find that the welfare of pensioners would be greatly enhanced if the guaranteed minimum return were applied to cumulative returns since inception of the scheme rather than to yearly returns. The small ensuing credit risk of pensioners on fund managers could be kept to a minimum by proper regulation; this would push fund managers to adopt safe constant proportionality portfolio insurance (CPPI) style investment strategies.
