By Alonso Peña
This e-book will introduce you to the most important mathematical types used to cost monetary derivatives, in addition to the implementation of major numerical versions used to unravel them. specifically, fairness, forex, rates of interest, and credits derivatives are mentioned. within the first a part of the publication, the most mathematical versions utilized in the realm of economic derivatives are mentioned. subsequent, the numerical equipment used to resolve the mathematical versions are offered. eventually, either the mathematical versions and the numerical tools are used to unravel a few concrete difficulties in fairness, foreign money, rate of interest, and credits derivatives.
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Extra resources for Advanced Quantitative Finance with C++
In literature, this set of equations is called a stencil. 3. Next collocate the stencil to all the nodes of the domain. We now apply the stencil to all the nodes in the domain with the exception of the nodes that represent the initial and boundary conditions. For these nodes, we know the value is a priori, and, hence, it does not need to be computed. [ 47 ] Numerical Methods 4. Iterate the solution in time with the stencil until we cover the full domain. In explicit FDM, you simply advance and compute the values for the unknown function u.
Using the stochastic models that we saw in the previous chapter to simulate one possible trajectory, with MC simulation, we are going to simulate many possible trajectories and, for each, compute the payoff that the contract would have had if the prices had followed that specific path in future. Afterwards, we are going to take all these possible payoffs and compute their expected value, that is, the mean or average value. This will give us an estimate of how much this contract will be worth in the future.
Equity Derivatives in C++ The full characteristics of the contract, the choice of the mathematical model, and its numerical method are shown below in the Bento Box template: DERIVATIVE CONTRACT 2 The underlying, being a stock, can be described using Geometric Brownian Motion (GBM): 3 Use Monte Carlo Simulation as a method for the computation of the value of the discounted expected payoff. NUM METHOD European Call option Barclays Bank PLC stock Counterparties are A and B. Underlying is Barclays stock.