You can always count on Espen Haug to deliver something thought provoking and in the September 2020 issue of Wilmott Magazine he does just that. Recent years have seen Espen focusing much of his attention on the boundaries of physics and as part of this journey we have the cover story ‘Space-Time Money’.
It is now normal to consider matters of finance in terms of microseconds (MIFID II, for example, requires microsecond timestamp precision in high-frequency trades) and nanoseconds (NASDAQ operates with timestamp resolution at one billionth of a second).
“In spite of these advances,” Espen writes, “the market for short duration loans has not taken advantage of the revolutionary developments in precision time-keeping technology. The shortest loans are overnight loans and their maturities are calculated on a different time scale than the one currently used for timestamps on security transactions. In terms of the technology itself, it is certainly possible to adjust the time scale for loan maturities to microseconds, or even below that, but to our knowledge no efforts have been initiated or completed yet. Nevertheless, in the future, we expect that the maturity time scale for short-term loans will shift to the time scale used in high-frequency trading, or lower. This article will explore these ideas around technology, time, and duration and will explain the implications for our concept of the time value of money.”
‘Swap rate a la stock: Bermudan swaptions made easy’
In ‘Swap rate a la stock: Bermudan swaptions made easy’ Dariusz Gatarek and Juliusz Jablecki show how Markovian projection together with some clever parameter freezing can be used to reduce a full-fledged local volatility interest rate model (such as Cheyette (1992)) to a “minimal” form in which the swap rate evolves essentially like a dividend-paying stock. Using a number of numerical examples the author compares such a minimal “poor man’s” model to a full-edged Cheyette local volatility model and the market benchmark Hull-White one-factor model. Numerical tests demonstrate that the “poor man’s” model” is in fact sufficient to price Bermudan interest rate swaptions. The main practical implication of this finding is that – once local volatility, dividend and short rate parameters are properly stripped from the volatility surface and interest rate curve – one can readily use the widely popular equity derivatives software for pricing exotic interest rate options such as Bermudans.
‘The Transport-based Mesh-free Method (TMM). A short review’
In ‘The Transport-based Mesh-free Method (TMM). A short review’ Jean-Marc Mercier and Philippe G LeFloch introduce a new numerical strategy which the authors refer to as the Transport-based Mesh-free Method (TMM) and discuss its applications to mathematical finance. The proposed method enjoys good accuracy properties similar to those obtained with integration formulas based on the Monte-Carlo methodology, and in particular enjoys quantitative error bounds which have important implications in applications. In this short review, the authors outline the main ideas behind this new strategy which relies on techniques of transportation and reproducing kernels. It leads the authors to an efficient method for numerical simulations while providing some light on the techniques currently developed by the artificial intelligence community. In the applications in the finance industry Mercier and LeFloch’s approach provides them with an accurate and fast algorithm, allowing the authors to compute various types of risk measures. Theoretical arguments are also put forward to justify the sharp convergence rates and almost optimal computational times that the authors observe in their numerical tests and, in addition, typical cases arising in finance applications support their claims. The problem of the curse of dimensionality in finance is briefly discussed.
‘Comparing Option Pricing Methods in Q’
In ‘Comparing Option Pricing Methods in Q’ Deanna Morgan and Sergei Kucherenko use kdb+ and the q language to compare the use of Monte Carlo (MC) and Quasi-Monte Carlo (QMC) methods for pricing options. Low-discrepancy Sobol sequences are used to price European and Asian options, using both incremental discretization and Brownian-bridge construction. Results are compared to the deterministic Black-Scholes price for each option type. Analysis was carried out using the time-series database, kdb+, from Kx. Kdb+ is a hybrid on-disk and in-memory columnar database, optimized for the ingestion, storage and analysis of huge amounts of structured data. Kx software is widely used in the financial industry, for streaming, real-time and historical analysis of market data. Our code makes use of the efficient and concise nature of the q language, to mirror the results shown in Kucherenko and Shah (2007).
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