Quantitative Finance Collector

This post has nothing to do with quantitative finance, so please skip it if you have no interest at all.

A friend of mine, who is an active animal protectionist, asked me if it is possible to embed a video on my blog. I didn't promise at the beginning worrying the video has nothing to do with my topic, but decide to do so after watching it, in addition, today is Sunday, take a rest then.

Dolphin is among the most intelligent animals and its often friendly appearance and seemingly playful attitude make it popular, I once read an article saying dolphin is as smart as an average three years kid, however, like many other animal species, it is under increasing human threat, as mentioned in Wikipedia, "In some parts of the world such as Taiji in Japan and the Faroe Islands, dolphins are traditionally considered as food, and killed in harpoon or drive hunts."

The video tells us how cruel the fishermen in Taiji are, how the activists hope to save dolphin but fail, a touching story worthy to think about.
PS: my friend is glad to add how happy he is after knowing Chinese government imposed a law recently against eatching dog meat in China, from now on it is illegal. A great step.

Below is the video, 90 minutes long, it is in English and with Chinese scripts.

Several good working paper have been found this week, hope you will also enjoy them.

1, Quant Nugget 1: Square-Root Rule, Covariances and Ellipsoids: How to Analyze and Visualize the Propagation Law of Risk in a Multi-Dimensional Market, "How to analyze and visualize the propagation law of risk in a multi-dimensional market.", http://papers.ssrn.com/sol3/papers.cfm?abstract_id=1548162;
2, Variance Swap Portfolio Theory, "Optimal portfolios of variance swaps are constructed taking account of both autocorrelation and cross asset dependencies. Market prices of variance swaps are extracted from option surface calibrations. The methods developed permit simulation of cash flows to arbitrary portfolios of variance swaps. The optimal design maximizes the index of acceptability introduced in Cherny and Madan (2009).", http://papers.ssrn.com/sol3/papers.cfm?abstract_id=1540815;
3, Efficient Options Pricing Using the Fast Fourier Transform , "The Fourier transform methods provide the valuable and indispensable tools for option pricing under L´evy processes since the analytic representation of the haracteristic function of the underlying asset return is more readily available than that of the density function itself. When used together with the FFT algorithms, real time pricing of a wide range of option models under L'evy processes can be delivered using the Fourier transform approach with highaccuracy, efficiency and reliability." http://papers.ssrn.com/sol3/papers.cfm?abstract_id=1534544;
4, Interest Rates and The Credit Crunch: New Formulas and Market Models , "We start by describing the major changes that occurred in the quotes of market rates after the 2007 subprime mortgage crisis. We comment on their lost analogies and consistencies, and hint on a possible, simple way to formally reconcile them. We then show how to price interest rate swaps under the new market practice of using different curves for generating future LIBOR rates and for discounting cash flows. Straightforward modifications of the market formulas for caps and swaptions will also be derived. " http://papers.ssrn.com/sol3/papers.cfm?abstract_id=1332205;
5, How Do Individual Investors Trade? , "This paper examines how high-frequency trading decisions (especially the choice of market versus limit orders) of individual investors are influenced by past price changes. Specifically, we address the question whether trading decisions to open or close a position are different in the case in which investors already hold a position than in the case in which they don't.", http://papers.ssrn.com/sol3/papers.cfm?abstract_id=1538760;
6, Optimisation in Financial Engineering , "We discuss the precision with which financial models are handled, in particular optimisation models. We argue that precision is only required to a level that is justified by the overall accuracy of the model. Hence, the required precision should be specifically analysed, so to better appreciate the usefulness and limitations of a model." http://papers.ssrn.com/sol3/papers.cfm?abstract_id=1547173

When asked how to value a stock option without dividend or with continuous dividend, many people would refer to Black Scholes formula, but how to price an option with discrete dividend then? certainly Black Scholes model can't be used directly since one of its assumptions is continuous payout. Paper Back to Basics: a new approach to the discrete dividend problem by Haug, Haug and Lewis summarizes the following ways:
1, Escrowed dividend model, which is the simplist and the least accurate way as a result. The basic idea of Escrowed dividend model is to adjust the current stock price by deducting the present value of future dividends, and plug in the replaced stock price to Black Scholes formula;
2, Chriss volatility adjustment model, besides replacing current stock price, this model adjusts volatility as well because the Escrowed dividend model alone decreases the absolute price standard deviation, hence underestimates an option's value. However, Chriss model yields too high volatility if the dividend is paid out early in the option’s lifetime, which generally overprices call options;
3, Haug & Haug volatility adjustment model; which is more sophisticated than Chriss model and takes into account the timing of the dividend, unfortunately, the authors show this method performs particularly poorly for multiple dividends stock option;
4, Bos volatility adjustment model, a even more sophiscated model than Haug & Haug, but still, it performs poorly for large dividends or long term options;
5, Lattice method, for example, non-recombining binomial tree introduced in the bible book Options, Futures, and Other Derivatives with Derivagem CD (7th Edition), we all know it is time-consuming;
6, Haug, Haug and Lewis method introduced in the above-mentioned paper, the basic idea is to calculate first the ex-dividend option price by Black Scholes model, then discount back the ex-dividend value under equivalent martingale measure. The authors demonstrate the high accuracy of their model with several examples afterwards.

Below is sample Matlab codes I wrote for comparision, a single dividend is used for simplicity, results similar to the table listed in the paper

Henry Merritt Paulson, Seventy-five men served as Treasury Secretary of the United States, blurted out when he learned U.K.'s Financial Service Authority was reluctant to approve a prebankruptcy deal for Barclays PLC to acquire Lehman, "The British screwed us."  This was revealed in Paulson's new book "On the Brink: Inside the Race to Stop the Collapse of the Global Financial System", where the author tell us the key decisions that had to be made with lightning speed under urgent market conditions, about Lehman Brothers, AIG, and other financial institutions.

Selected author's note from the book On the Brink: Inside the Race to Stop the Collapse of the Global Financial System:

Most recent job offers from Quant jobs board:

Scientific programmersCBCS in Cambridge MA  
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PHD Internships at Bank of England in London            
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