Quantitative Finance Collector

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Stochastic volatility models, specifically, Heston model, SABR model, are introduced before and become the widely used among academia and industry. However, the calibration process is difficult because generally the pricing requires numerical integration, and calibration requires to find five and eight parameters instead of only one for Black Scholes model.

Found a paper Calibrating Option Pricing Models with Heuristics, where the author look into the calibration of Heston (1993) and Bates (1996) models. Finding parameters that make the models consistent with market prices means solving a non-convex optimisation problem. Optimisation heuristics is suggested for this issue, more specifically they show that Differential Evolution and Particle Swarm Optimisation are both able to give good solutions to the problem.

Take a look if you are interested, in the Appendix the R and Matlab codes are given for a better understanding. http://papers.ssrn.com/sol3/papers.cfm?abstract_id=1566975

Following Value at Risk xls and var backtesting, a third post about using historical simulation for Value at Risk calculation. We know one shortcoming of historical simulation is: the result highly depends on the choice of sample data length, VaR result does not vary often or changes suddenly. Despite this weakness, HS is still popular due to its obvious advantage: easy to implement, and no distribution assumption required, which is especially appealing if the estimate of distribution assumption is difficult. Several ways have been proposed to improve HS's performance, here are two selected methods with good results I personally use.

1, The Best of Both Worlds: A Hybrid Approach to Calculating Value at Risk by Jacob Boudoukh1, Matthew Richardson and Robert F. Whitelaw. By hybrid it means this approach is a combination of RiskMetrics's parametric method and Historical Simulation. The basic idea is: since we can allocate larger weight to recent data and smaller weight to remote data for exponential weighted moving average (EWMA) volatility calculation, hence improves the backtesting performance of parametric method, why can't we then apply a similar principle to historical simulation? make sense? so it estimates the VaR of a portfolio by applying exponentially declining weights to past returns and then finding the appropriate percentile of this time weighted empirical distribution. The following results are from the paper The Best of Both Worlds: A Hybrid Approach to Calculating Value at Risk, page 11. It does improve compared with the vanilla historical simulation and EWMA parametric method, nice.

Friday again, just a final kind remind, since Change of Friday Reading List Setting, I have been updating Friday reading list on page articles, for example, the list of this week includes:
1, Testing for Asymmetric Dependence, http://www.bepress.com/snde/vol14/iss2/art2/;
2, Index-Exciting CAViaR: A New Empirical Time-Varying Risk Model, http://www.bepress.com/snde/vol14/iss2/art1/;
3, Improving Portfolio Selection Using Option-Implied Volatility and Skewness , http://papers.ssrn.com/sol3/papers.cfm?abstract_id=1559642;
4, Trading Activity and Bid-Ask Spreads of Individual Equity Options, http://papers.ssrn.com/sol3/papers.cfm?abstract_id=1553222;
5, The Method of Simulated Quantiles, http://papers.ssrn.com/sol3/papers.cfm?abstract_id=1561185

Keep an eye on page articles.

An interesting application of Inverse Graphing Calculator, where you enter any word from A to Z into your calculator and then get a graph of the curve.

For instance, if you write an equation:


you would get a graph below:


Creat your own at http://www.xamuel.com/inverse-graphing-calculator.php