Gelman, Stat Modeling, On Blogging, here. Like the guy in the comments who says Clive James drags on, nice work.
The necessary conceit of the essayist must be that in writing down what is obvious to him he is not wasting his reader’s time. The value of what he does will depend on the quality of his perception, not on the length of his manuscript. Too many dull books about literature would have been tolerably long essays; too many dull long essays would have been reasonably interesting short ones; too many short essays should have been letters to the editor. If the essayist has a literary personality his essay will add up to something all of a piece. If he has not, he may write fancily titled books until doomsday and do no good. Most of the criticism that matters at all has been written in essay form. This fact is no great mystery: what there is to say about literature is very important, but there just isn’t all that much of it. Literature says most things itself, when it is allowed to.
In this talk we will introduce the particle method and show how it solves a wide variety of smile calibration problems: – calibration of the local volatility model with stochastic interest rates – calibration of stochastic local volatility models, possibly with stochastic interest rates and stochastic dividend yield – calibration to the smile of a basket of multi-asset local volatility -local correlation models, possibly with stochastic volatility, stochastic interest rates, and stochastic dividend yields – calibration of path-dependent volatility models and path-dependent correlation models.
The particle method is a Monte Carlo method where the simulated paths interact with each other to ensure that a given market smile is fitted. PDE methods typically do not work for these high-dimensional models. The particle method is not only the first available exact simulation-based method. It is also robust, easy to implement, and fast (it is as fast as a standard Monte Carlo algorithm), as many numerical examples will show. As of today, it is the most powerful tool for solving smile calibration problems. Icing on the cake for those who like maths: there are nice mathematics behind the scenes, namely the theory of McKean stochastic differential equations and the propagation of chaos.
Felix Salmon, Reuters, Whither bond returns? here.
El-Erian explains that the consistent and gratifying numbers posted by fixed-income portfolios were the result of a “virtuous circle”, where four different drivers all fed each other and helped push returns upwards:
- A secular fall in interest rates;
- A consistently negative correlation between fixed-income returns and equity returns, over a six-month time horizon;
- Monster flows into the asset class;
- Direct support from central banks.
Now, however, those four drivers are coming to an end. Interest rates are at zero; they can’t fall any lower. Over the long term, they have nowhere to go but up. Total assets in fixed-income profiles rose from $4.7 trillion in 1998 to $12.1 trillion at the beginning of 2013 — but now flows have turned negative, and investors are pulling their money out of bonds. And while the Fed is still spending some $85 billion a month buying bonds in the secondary market, that isn’t going to last forever: the taper is coming, sooner or later.