This is Monte Carlo Application that uses various Options/FDM/RNG/PRICER
Name: William Zhang
The FDM option pricing application is for pricing various options such Asian, European and Barrier Option using various Finite Difference method. The application allows the user to input various Option pricing parameter such as stock price, strike price, risk-free interest rate to price options using the various Finite Difference Methods. The application even allows the user to use various Random number generators such as Mersenne Twister, Polar Masglia and Bob Mueller. Finally, the user can input the data by console or by putting the data inside the input.csv. It allows users to store info into the azure database and output the data to the same database.If the user wishes to put more than one option dataset parameters, then the user should put the data into the input.csv file.
The user can see the class diagram hosted inside in the Solution Explorer, by opening the project solution folder and by viewing the "ClassDiagram.cd" file. The following are a set of description of the various classes used in the application.
This class essentially generates a random number that follows a normal distribution with mean zero and variance one. The user can select between various generators such as Mersenne Twister, Polar Masglia and Box Mueller. The latter two transforming uniform random numbers from zero to one to a normal distribution with polar form.
This class specifies which types of stochastic differential equation that the user wants. The user is able to choose between the contrast elasticity variance model (CEV) and the Geometric Brown Motion Differential equation (GBM). The former being similar to GBM but there is a specified Beta that model the elasticity of volatility in relation to stock price.
This class solves the specified Stochastic differential equation by allowing the user to choose the various Finite difference methods to solve the differential equation. The user can use choose explicit Euler, Balanced Midpoint, and Milstein Method to solve the differential equation.
This class models the various types of options that the user can choose. Different options have different payout schemes. The user can choose between the various option such as the classical European, The Asian, or Barrier Options.
This class essentially coalesces all the various the parts the user want and builds the appropriate RNG,SDE,PRICER,and FDM objects to start the Finite Difference method simulation . The parts are created and stored into a tuple for convience.
The parts made from the Builder class must be mediated because the parts made from Builder class have complex interactions. Therefore, we have a mediator to resolve these interactions inside a STRUCT to generate an output. The nested loop side the start function is parallelized with OMP to improve speed.
This header file is the application input point and is by far the largest file. This file allows the user the start the application and allows the user to choose input data by console,by File, or database. The user also must specify the #NSIM and #SUBIDVISION as well as which parts they want in the application. This is where the mediator does most of its work.
Most of the work performed is the double for loop inside the Mediator start function. So in general the time complexity of this program is O(NSIM* SUBDVISIONS). Which is quadratic in time complexity and in general has a solution convergence that is linear. For inputs NSIM*subdivisions >= 5,000,000 performance to starts to deteriorate. Therefore we incorporated multi-threading that is provided by OMP parallelization library. Across all option parameter inputs the NSIM was 1,000,000 and subdivisions steps were 500 As evidence for the running time, run the application with the default parameters provided in the input.csv
WITHOUT MULTITHREADING: Avg Time to completion : 90.6-98 seconds NSIM: 1000000 NT:500
Total time: 87.0217 Output # 1 Price: 5.71458
Total time: 92.582 Output # 2 Price: 2.2088
Total time: 98.522 Output # 3 Price: 7.7895
Total time: 90.39 Output # 4 Price: 94.1845
Total time: 89.9149 Output # 5 Price: 1.22124
Total time: 89.6994 Output # 6 Price: 4.04489
Total time: 98.1227 Output # 7 Price: 0.209067_
With Multithreading (OMP) Avg Time to completion: 32-42 seconds NSIM: 1000000 NT:500
Total time: 29.0217 Output # 1 Price: 5.71458
Total time: 31.5582 Output # 2 Price: 2.2088
Total time: 32.5722 Output # 3 Price: 7.7895
Total time: 34.639 Output # 4 Price: 94.1845
Total time: 34.9149 Output # 5 Price: 1.22124
Total time: 36.6994 Output # 6 Price: 4.04489
Total time: 37.4527 Output # 7 Price: 0.209067
As you can see here the performance was increased by 50 percent with OMP parallelization tools. The user can choose his own parameter schemes to check the accuracy of the application. I also tested the version with Asian options and maintained 0.02 - 0.03 cent accuracy. And here is CD provided by the MSVC.
- The user must have MSVC C++ as well install boost libraries. Here is the link to boost and visual studio 2017. But the user should install the lastest version of their respected software https://www.badprog.com/c-boost-setting-up-on-windows-10
- If the user wants to use other C++ editors then the user should also install and link omp seperately as well as text editors that supports msvc compiler for C++ https://www.geeksforgeeks.org/openmp-introduction-with-installation-guide/
- Once you are done with either or both steps, clone the repository with the provided link above.
- Start the application by running the .exe file or clicking "start without debugging in C++" in microsoft visual studio code.
- If the user wants to put in multiple set of option parameter inputs, then the user has to modify the "input.csv" files provided in the project directly. From there, you will be able to modify the parameter of your option prices
- The user can instead opt out and type all the parameters of the option price by console instead.
- The user will first be prompted to choose between the random number generator type, finite difference method type and the the model for the stochastic differential equation. The user will also have to specify the number of time steps and number of subdivisions. Note that larger subdivision and time steps lead to slower computation times.
- If the user wants to type in the input for a single set of option parameter than the user will be prompted to do so.
- The simulation wil begin after the user has done steps 4-8. If the user put their inputs inside the "input.csv" the the output will be printed out on "Output.csv" as well as on the console.
- The option prices and simulation number will printed for convience.
If the user wants to add additional finite difference methods scehemes, stochastic diffierential equations,random number generator types or add additional types of options for this application then fork over the repository and make the necessary changes. The user must directly inherit from the classes that The application is not limited to option prices. There are various Stochastic differential equation that need to be solved from various engineering problems such as calculating the total price of a home heating syste,. SDE are not only applicable to risk free finance but other related fields that need to compute equations that have more than one stochastic term. Here is an article and see if your engineering problem has a stochastic differential equation that needs to be solved .https://en.wikipedia.org/wiki/Stochastic_differential_equation