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Quantitative finance is the use of frontier mathematical and statistical models with extremely large datasets to analyze financial markets and securities. Common examples include (1) the pricing of derivative securities such as options, and (2) risk management, especially as it relates to portfolio management applications.

Machine learning is an increasingly important and controversial topic in quantitative finance. A lively debate persists as to whether machine learning techniques can be practical investment tools. Although machine learning algorithms can uncover subtle, contextual, and nonlinear relationships, overfitting poses a major challenge when one is trying to extract signals from noisy historical data.

There are very few things which we know, which are not capable of being reduced to a Mathematical Reasoning, and when they cannot, its a sign our Knowledge of them is very small and confused.

Where a mathematical reasoning can be had, it’s as great folly to make use of any other, as to grope for a thing in the dark when you have a Candle standing by you.

Portfolio optimization is not the only possible way of building a portfolio. Several modern financial technologies like Machine Intelligence, Data Science and Advanced Analytics are available as a new kind of math to work with the level of uncertainty.

Adding assets with low correlations to a portfolio can decrease the total risk without any loss in potential returns. When I increase the diversity within investments, it results in a higher Sharpe Ratio.

At Global Accountancy Institute, We now apply mathematical and computational methods to develop and exploit financial opportunities for return enhancement and risk control in the Global Financial Markets.

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In its third edition, this book presents the most significant equitya derivatives models used these days. It is not a book around esoteric or cutting-edge models, but rather a book on relatively simple and standard models, viewed from the angle of a practitioner.

A few key subjects explained in this book are: cash dividends for European, American, or exotic options; issues of the Dupire local volatility model and possible fixes; finite difference techniques for American options and exotics; Non-parametric regression for American options in Monte-Carlo, randomized simulations; the particle method for stochastic-local-volatility model with quasi-random numbers; numerical methods for the variance and volatility swaps; quadratures for options under stochastic volatility models; VIX options and dividend derivatives; backward/forward representation of exotics.

The January 2021 third edition adds significant details around the physical exercise feature, how to imply the Black-Scholes volatility, the projected successive over-relaxation as well as the recent policy iteration method for the pricing of American options (particularly relevant in the case of negative interest rates), the Andersen-Lake algorithm as fast pricing routine for the case of vanilla American options under the Black-Scholes model, random number generation, antithetic variates, the vectorization of the Monte-Carlo simulation, RBF interpolation of implied volatilities, the Cos method for European option under stochastic volatility models, the Vega in stochastic volatility models.

The new text also includes important corrections around the pricing of forward starting and knock-in options with finite difference methodsicon

 

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