Software Libraries for Math, Finance and Computer Science

An algorithm for inserting a sorted vector of pairs into a map In a naively programmed map this causes worst case performance for the tree. For a binary tree, which does not rebalance, inserting a sorted list, causes the binary tree to have a depth of N, where N is the number of items in the sorted vector.

Stable Quick Sort algorithm encoded as a template class.

The Newton Raphson algorithm coded as a class template. This encapsulation allows for:

• the function to be zeroed, to be represented as a member function pointer
• the derivative to be represented as a member function pointer
• the second derivative is an optional parameter which can speed convergence
• the upper and lower boundaries of the domain can optionally be specified
• the derivative can be calculated twice per iteration, to increase the speed of convergence. This is useful, if the derivative is faster to computer, than the function itself

The Secant algorithm coded as a class template. This encapsulation allows for:

• the function to be zeroed, to be represented as a member function pointer
• the upper and lower boundaries of the domain can optionally be specified

The Grid Search algorithm coded as a class template. This encapsulation allows for:

• the function to be maximized/minimized, to be represented as a member function pointer
• the upper and lower boundaries of the domain can optionally be specified
• both the maximum and minimum are solved

The Black Scholes formula coded as a class. This encapsulation allows for:

• Stocks, stock indexes, futures and cash options to be represented with the same formulae. Each underlying has the same formula, but different values of alpha:
  1. For stocks and stock indexes, alpha = r - dividend yield.
  2. For futures alpha = 0
  3. For currencies alpha = the foreign interest rate
• A large number of derivatives to be calculated
• very fast calculation because the Cumulative Normal distribution, is calculated with the approximations from Abromowits and Stegun
• The formulae are described here

This class, "american_fudge" is a child class of the European_option_pair with a fudge factor so that the exercise boundaries match up with American options. This approximation is much faster than the binomial method.

This class, "american_option_approximation" is a child class of the European_option_pair . The option value is determined by do a grid search on T, in the range 0<=T<=Tau, and using the European option, with the maximum value.

The binomial option pricing algorithm . This encapsulation is a very minimual version of the binomial option pricing algorithm, with many virtual functions, which can be overloaded for more specilized option pricing methods. Alpha is an input variable, so stocks, stock indexes, futures and currencies, can all be the underlying.

Sample Programs

Sample Program which illustrates 4 different option valuation models.

Sample Program which illustrates how to calculate implied volatility with 4 different option valuation models.

Sample Program which illustrates the Newton Raphson algorithm.

Sample Program which illustrates the Secant algorithm.