"The Contributions of Professors Fischer Black, Robert Merton, and Myron Scholes to the Financial Services Industry"

This paper is written as a tribute to Professors Robert Merton and Myron Scholes, winners of the 1997 Nobel Prize in economics, as well as to their collaborator, the late Professor Fischer Black. We first provide a brief and very selective review of their seminal work in contingent claims pricing. We then provide an overview of some of the recent research on stock price dynamics as it relates to contingent claim pricing. The continuing intensity of this research, some 25 years after the publication of the original Black-Scholes paper, must surely be regarded as the ultimate tribute to their work. We discuss jump-diffusion and stochastic volatility models, subordinated models, fractal models, and generalized binomial tree models, for stock price dynamics and option pricing. We also address questions as to whether derivatives trading poses a systemic risk in the context of models in which stock price movements are endogenized, and give our views on the "LTCM crisis" and liquidity risk.

Estimating long-term volatility parameters for market-consistent models

Contemporary actuarial and accounting practices (APN 110 in the South African context) require the use of market-consistent models for the valuation of embedded investment derivatives. These models have to be calibrated with accurate and up-to-date market data. Arguably, the most important variable in the valuation of embedded equity derivatives is implied volatility. However, accurate long-term volatility estimation is difficult because of a general lack of tradable, liquid medium- and long-term derivative instruments, be they exchange-traded or over the counter. In South Africa, given the relatively short-term nature of the local derivatives market, this is of particular concern. This paper attempts to address this concern by: — providing a comprehensive, critical evaluation of the long-term volatility models most commonly used in practice, encompassing simple historical volatility estimation and econometric, deterministic and stochastic volatility models; and — introducing several fairly recent nonparametric alternative methods for estimating long-term volatility, namely break-even volatility and canonical option valuation. The authors apply these various models and methodologies to South African market data, thus providing practical, long-term volatility estimates under each modelling framework whilst accounting for real-world difficulties and constraints. In so doing, they identify those models and methodologies they consider to be most suited to long-term volatility estimation and propose best estimation practices within each identified area. Thus, while application is restricted to the South African market, the general discussion, as well as the suggestion of best practice, in each of the evaluated modelling areas remains relevant for all long-term volatility estimation

Markov Functional Market Model nd Standard Market Model

The introduction of so called Market Models (BGM) in 1990s has developed the world of interest rate modelling into a fresh period. The obvious advantages of the market model have generated a vast amount of research on the market model and recently a new model, called Markov functional market model, has been developed and is becoming increasingly popular. To be clearer between them, the former is called standard market model in this paper. Both standard market models and Markov functional market models are practically popular and the aim here is to explain theoretically how each of them works in practice. Particularly, implementation of the standard market model has to rely on advanced numerical techniques since Monte Carlo simulation does not work well on path-dependent derivatives. This is where the strength of the Longstaff-Schwartz algorithm comes in. The successful application of the Longstaff-Schwartz algorithm with the standard market model, more or less, adds another weight to the fact that the Longstaff-Schwartz algorithm is extensively applied in practice

Modelling the implied volatility of options on long gilt futures

This paper investigates the properties of implied volatility series calculated from options on Treasury bond futures, traded on LIFFE. We demonstrate that the use of near-maturity at the money options to calculate implied volatilities causes less mis-pricing and is therefore superior to, a weighted average measure encompassing all relevant options. We demonstrate that, whilst a set of macroeconomic variables has some predictive power for implied volatilities, we are not able to earn excess returns by trading on the basis of these predictions once we allow for typical investor transactions costs

Practical volatility and correlation modeling for financial market risk management

What do academics have to offer market risk management practitioners in financial institutions? Current industry practice largely follows one of two extremely restrictive approaches: historical simulation or RiskMetrics. In contrast, we favor flexible methods based on recent developments in financial econometrics, which are likely to produce more accurate assessments of market risk. Clearly, the demands of real-world risk management in financial institutions - in particular, real-time risk tracking in very high-dimensional situations - impose strict limits on model complexity. Hence we stress parsimonious models that are easily estimated, and we discuss a variety of practical approaches for high-dimensional covariance matrix modeling, along with what we see as some of the pitfalls and problems in current practice. In so doing we hope to encourage further dialog between the academic and practitioner communities, hopefully stimulating the development of improved market risk management technologies that draw on the best of both worlds

The least squares method for option pricing revisited

It is shown that the the popular least squares method of option pricing converges even under very general assumptions. This substantially increases the freedom of creating different implementations of the method, with varying levels of computational complexity and flexible approach to regression. It is also argued that in many practical applications even modest non-linear extensions of standard regression may produce satisfactory results. This claim is illustrated with examples