# American Option pricing with Bayesian Monte Carlo Path

Version 29.0.0.1 (194 KB) by
Density Functional American Option pricing with Bayesian Monte Carlo Path Int & MUSIC w/ Kelly Criterion
Updated 5 Mar 2021

Multipath computation of American option prices and confidence limits based on statistics
A probability distribution is calculated from a past stock chart and the fat tails are estimated. The distribution , unique to every stock chart, is used to generate an arbitrary number of paths into the future (3000 by default) and 50% and 80% and 98% confidence intervals are calculated and displayed. A computation of the most probable call to put ratio is calculated and used to generate a Most Probable Win percentage per day. The final absolute probability of winning at the 98% level is used to calculate the Kelly Criterion multiplied by 0.92 in the Risk Analysis section of the figure. This simulation differs significantly from Black Scholes and is more accurate. Every stock has its own probability distribution in the past. Care should be taken to note that market conditions can change abruptly in the future and distributions can be significantly altered over a short time frame by global market events, Intra-day distributions can be remarkably different from end of day distributions, so the results may vary from real world trading but it is probably the most accurate look ahead in stable markets that we are going to get with a mathematical approach. Care and attention to liquidity , volume and volatility should be observed.
Stock Forecasting and American Option pricing compared to Black- Scholes(BS) using Bayesian Markov Monte Carlo Simulation and Wavelet or Fourier or Neural Network Extrapolation with Indicators..http://library.wolfram.com/infocenter/MathSource/9086/ for more information!
If you use the alternate program as well, Bayesian Markov Stochastic Monte Carlo Valuation of Integrated Price Volume Action with Kelly Criterion, the kelly values from that program should be more accurate as an assessment of volume trends are also incorporated and we all know how important liquidity is. An expert using both programs will be a better judge just before an earnings announcement. A Fourier extrapolation is also carried out, but is only valid if it is supported in the range by the Statistical look ahead! The extrapolation is important for assessment of trends and cycles!

### Cite As

Chondrally (2024). American Option pricing with Bayesian Monte Carlo Path (https://www.mathworks.com/matlabcentral/fileexchange/56352-american-option-pricing-with-bayesian-monte-carlo-path), MATLAB Central File Exchange. Retrieved .

##### MATLAB Release Compatibility
Created with R2016b
Compatible with any release
##### Platform Compatibility
Windows macOS Linux

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Version Published Release Notes
29.0.0.1

Updated to reflect correct Toolbox dependencies

29.0.0.0

changed title

28.0.0.0

updated coeffs in generateTemperatures, to reflect proper linear trend into future
and updated offset at end of program in MusicFinal. adjusted getpercenterrorlinear and optionprices.m
so coefficients would be passed without error....
updated to R2016b

27.0.0.0

updated description
updated MusicFinal.m to correct initial prediction value to be correct value based on last data point of original data

26.0.0.0

updated tiltle to include Density functional , i use a probabilty density functional to compute the path integral

25.0.0.0

updated expiration date

24.0.0.0

updated all kelly criterion formulas with error checking

23.0.0.0

updated musicfinal
updated MusicFinal to make it more accurate added Matrix G=conj(transpose(eigvecs matrix)).(eigvecs matrix)

22.0.0.0

added two profit graphs, one for most probable profit and one for fourier path profit
added edit boxes for all 4 legs of a sophisticated option strategy
updated the code to calculate the complete kelly criterion

21.0.0.0

updated optionprices, musicfinal and kelly criterion calculation included plot of fourier fit to data

20.0.0.0

updated musicfinal and added getpercenterrorlinear3 to fix scaling of fourier output

19.0.0.0

updated kelly criterion and figure
updated summary

18.0.0.0

added one last line to MusicFinal y = y - y(N2)+s0 to fix discontinuity at boundary

17.0.0.0

u[pdated MusicFinal to fix discontinuity at boundary condition
updated call and put present value plots with magenta fourier information
updated figure to include fourier call and put option values

16.0.0.0

updated title
updated title
sign change in fourier trend analysis
modified equation

15.0.0.0

introduced MUSICFINAL subroutine and corrected fourier trend analysis

14.0.0.0

fixed volatility presentation and updated figure display

13.0.0.0

updated color of calculate plots button to make it more noticeable
added EMA40 Volume indicator as a measure of recent liquidity

12.0.0.0

changed default number of paths to 3000

11.0.0.0

updated kelly call and kelly put criterion

10.0.0.0

updated figure

9.0.0.0

added edit box to figure and matlab code to calculate the ratio of EMA 40 days to EMA 200 days, a critical ratio for trading.

8.0.0.0

updated magnitude calculation of spectral components
forget most recent zip file

7.0.0.0

corrected magnitude of spectral components in rootmusic fourier so that amplitudes of black time series would be commensurate with data spectral components.

5.0.0.0

added phase to rootmusic fourier so that timing of trend in stock chart will continue appropriately

4.0.0.0

forgot to add new zip file last time, updated black rootmusic fourier mag and phase
updated requirements.... needs curve fitting toolbox, financial toolbox, signal processing toolbox and matlab
added rootmusic fourier mag and phase of extended time series to most probable path plot

3.0.0.0

updated documentation
updated kelly criterion to represent absolute percent win probability
updated kelly criterion description in documentation

2.0.0.0

Changed way risk analysis is reported to make it more intuitive

1.0.0.0

included a more realistic description of real markets
made a mistake about what matlab products were required. Only the financial toolbox and matlab R2016a are required.
corrected volatility calculation
corrected volatility calculation
a note about functionality
changed volatility calculation from cubPCR1 cubic interpolation volatility to black scholes volatility