WILMOTT Magazine May 2023 – Black-Scholes 50th Anniversary Issue Part 1

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The May 2023 issue of WILMOTT Magazine celebrates 50 years since the publication of the papers by Fischer Black, Myron Scholes and Robert Merton on the valuation of options. We have brought together some famous names to give their views on the impact and the accuracy of this model, perhaps the only successful model in economics.

Wilmott, Paul – The Marketing Department’s Derivation of Black-Scholes-Merton: An alternative history from a parallel universe There are many derivations of the Black-Scholes-Merton partial differential equation and formulæ for the value of derivatives. Some are easy to understand, some are not. Some are easy to generalize, some are not. But to my knowledge only one derivation comes from a collaboration between someone wearing a fine pair of Crockett & Jones, and the other definitely not.

Lewis, Alan – The Limit Where Black-Scholes “Works” The seminal (Black and Scholes, 1973) publication celebrated in this issue introduced a (stock price evolution) model and an (option value) formula—two ideas worth distinguishing. Nowadays, the formula is used to represent option prices via an implied volatility, IV (T, K), where T is a time-to-maturity and K is a strike price. The formula is very useful. At the same time, because of the K-dependence, the model is strongly rejected in statistical tests. However…

Lipton, Alexander and Reghai, Adil – SPX, VIX and Scale-Invariant LSV Local Stochastic Volatility (LSV) models have been used for pricing and hedging derivatives positions for over 20 years. An enormous body of literature covers analytical and numerical techniques for calibrating the model to market data. However, the literature misses a potent approach commonly used in physics and works with absolute (dimensional) variables rather than with relative (nondimensional) ones. 

Gatarek, Dariusz – The Principle of Two Models: the Cases of Black-Scholes Formula for Interest Rates and of Gaussian Copula for Credit In this article, I try to show that a given market segment needs at least two models: one as a pricing convention and one to run the portfolio of securities. These models should be related in such a way that the model to manage the books is an extension of the pricing convention. Financial modeling succeeded in the case of options, but it failed with the CDOs, resulting in the credit crunch.

Boyle, Phelim – How Black Scholes Changed My Life Why the option model became the dominant paradigm of the author’s career.

Hull, John – Why Has Black-Scholes-Merton Been So Successful? It is not because the model is a really good description of the way options are priced by the market.

Bouchaud, Jean-Philippe – Welcome to a post Black-Scholes World Black-Scholes is simultaneously extraordinarily important and woefully flawed.

Schoutens, Wim – A Contemporary View on the Golden Anniversary of the Celebrated Black-Scholes-Merton Model Luckily, in 1973, normality was normal.

Andreasen, Jesper – Holes in Black-Scholes? In this article, we provide a model-free test for whether the dynamic hedging argument actually works in practice and a quantification of how much jumps influence the delta hedge.

Ballabio, Luigi – The Black-Scholes Model in QuantLib Any remaining errors are our fault, not theirs.

Alexander, Carol – Can you Beat Black-Scholes at Delta Hedging? Not a bad question given Black-Scholes assumes zero correlation between underlying price and volatility, the consequence of which is an entirely flat volatility surface.

Wystup, Uwe – Quick and Dirty – Short Cuts for Option Lovers Highlighting a few shortcuts in option pricing, in the spirit of sanity checks, quick answers, and passing interview questions.

Elsewhere this issue …

Brown, Aaron – The Hunting of the Snark For people who want to understand what zk-SNARKs are, why they are important, how to use them safely, and what the future might hold; without unnecessary technical detail.

Poulsen, Rolf – We Hold These Truths not to be Self-evident, Part 3: Mission Impossible?
In Math, you can prove a negative. Let’s take a look at some mostly model based examples.

Das, Satyajit – Alice Through The Crypto Glass: Part 4 Bringing this series to a close, the author considers potential applications of blockchain technology.

Giller, Graham – Yes, Quants Should Care about Money Left on the Table What if, in some way, we had access to some counterfactual measure of how well we could have done with our trading?

Kelly, Michael – Financial Time Series In this article, we will focus on the time series data which is the basis of all financial analysis, and which can be encapsulated with the functions TimeSeries, for single series, and TemporalData, for a collection of time series.

Balan, Priya – Designing Banking Book balance forecasting models to support multiple use cases Part II In this article, we discuss the design framework for a single model for a portfolio of similar Banking Book products shared across all use cases requiring balance or associated forecasts in detail.