SABR Calibration: A simple, explicit initial guess
The SABR model is widely used, particularly in the interest rate world, to help manage the volatility smile. Depending on 4 parameters, \(\alpha\), \(\beta\), \(\rho\) and \(\nu\), often \(\beta\) is...
View ArticleLamperti Transform
Let \(X_t\) be an Ito process given by $$dX_t=f(X_t,t)dt+\sigma(X_t,t)dw_t$$ The Lamperti transformation is, $$Z_t=\phi(X_t,t)=\int\frac{1}{\sigma(x,t)}dx$$ and has a unit diffusion; that is,...
View ArticleYear End Turn Rates
The year-end turn-rate (or the turn-of-the-year rate) is the interest rate for the period between the last business day of the year until the first good business day in the next year. For example, in...
View ArticleInitial Margin and Swap Pricing
Welcome to 2015 everyone! I thought I’d start the year with some simple thoughts on Initial Margin, before later applying these to what may (or may not!) be charged when dealers quote on a compression...
View ArticleSwap Curve and Fly Trading: What goes in, must come out
Curve and Fly trading looks like a simple old game – existing trades are ripped-up and replaced with spot-starting hedges. So why don’t people do that across the Bloomberg SEF? Curve and Fly Trades...
View ArticleComputus: Algorithms to compute Easter
With Easter arriving this weekend, I thought it might be interesting to mention something on the algorithms used to compute Easter. As we know, Easter is a not a fixed date each year, it is determined...
View ArticleOIS Swap Nuances
Overnight Indexed Swaps (OIS) are fixed-float swaps where the floating leg index is a compounded overnight interest rate. For short dated swaps, those less than 1Y, the coupon structure is usually zero...
View ArticleMechanics of Asset Swaps and Government Bond Swap Spreads
Last week we looked at the US Markets and Spreadovers, that trade as a spread to underlying US Treasury bonds. These are not the only structures that trade in the market. Other currencies and other...
View ArticleCME-LCH Basis – What does the Term Structure tell us?
We analyse the CME-LCH Basis volumes by tenor and look at what the forward curve implies for prices in the future. There are no signs of normalisation trades in the market, with the basis widening over...
View ArticleSwap Equivalents via Waves
In a recent paper, “Calculating Delta Risks and Hedges via Waves (2015)“, Hagan deals with an old practical problem–determining risk and hedges on an interest rate book. In older systems a delta hedge...
View ArticlePrincipal Component Analysis of the Swap Curve: An Introduction
Principal Component Analysis (PCA) is a well-known statistical technique from multivariate analysis used in managing and explaining interest rate risk. Before applying the technique it can be useful to...
View ArticleQuantitative Finance ‘GoodReads’
Two reading lists of books relevant to quantitative finance are provided using the GoodReads platform. Often I am asked to recommend good books to help a student, colleague or customer get a better...
View ArticleValuation of Massive OTC Portfolios: From Milli-Seconds to Micro-seconds
In the not to distant past I can recall seeing several risk systems valuing vanilla interest swaps with individual trade valuations taking around a few milliseconds. Whilst quants might rightly be...
View ArticleFed Fund Swap Nuances
A few people have recently asked me about the details of USD Fed Fund Swaps. I collected some of my answers together in this post for convenience. Fed Fund Swap and OIS Swap differences Fed Fund Swaps...
View ArticleArbitrage-Free SABR: Finite Difference Techniques
In January a new approach to the SABR model was published in Wilmott magazine, by Hagan et al., the original authors of the well-known SABR model. They review some of the weaknesses of the model, and...
View ArticleSABR Calibration: A simple, explicit initial guess
The SABR model is widely used, particularly in the interest rate world, to help manage the volatility smile. Depending on 4 parameters, \(\alpha\), \(\beta\), \(\rho\) and \(\nu\), often \(\beta\) is...
View ArticleAdapting to Direct Forward Curves
In interest rate pricing direct forward curves are defined on forward rates for a specific tenor as opposed to the more common discount factor representation, or the instantaneous forward curve...
View ArticleSDR Prices, Python and plotly
We supply simple code to retrieve SDR Prices into Python And create a streaming chart of swap prices and volumes The code was written by an ex-trader with no prior experience of Python Showing how easy...
View ArticleData correction with fuzzy string matching
We are all familiar with Google’s “Did you mean” correction for misspelt search terms. But how does it work? There is a great chapter by Norvig in the book ‘Beautiful Data: The stories behind elegant...
View ArticleAuto-detecting date format in CSV files
When uploading data into systems, comma separated value format (CSV) is a common choice. A difficulty can arise when editing CSV files in Excel — date formats can easily (and accidentally) change...
View Article
