Ill Posed Black-Scholes-Merton Equation

Run a demo

Run python test.py.

NOTE

This module is mathematically sound and ready to be deployed. The README file will be updated with instructions will be updated very soon.

Usage

Datablock

A datablock represents three consecutive days of option ask and bid price, the corresponding stock ask and bid price of the day, and three consecutive days of implied volatility. A datablock is declared as follows:

block = ns.DataBlock(today='10/19/2016',\
                       option_ask = [0.86, 0.86, 0.86],\
                       option_bid = [0.84, 0.85, 0.85],\
                       volatility = [39.456, 38.061, 37.096],\
                       stock_ask = 4.66,\
                       stock_bid = 4.65)

System generation

Once three days of data are loaded in a block, the system to be solved is ready to be generated. It takes to specify the size of the matrix to fill, and the regularization parameter $\beta$:

m = 15
beta = 0.01
block.create_system(m, beta)

System resolution

When the matrix is created and filled, the Datablock class implements its resolution:

result = block.solve()

Solution reshape

The solution needs to be reshape for a more consistent usage:

solution = result.x.reshape((m-1,m-2))
print('Minimizer is:')
print(solution)
print('Estimates for 1tau and 2tau: ', solution[[math.ceil(m/2-1), m-2], math.ceil((m-2)/2)])

Trading strategy

If the number returned by solution[[math.ceil(m/2-1), m-2], math.ceil((m-2)/2)] are greater than the ask price for tomorrow and the day after tomorrow plus $0.03, we need to buy 5000 or 10000 options to sell them tomorrow and the day after tomorrow. More precisely:

if solution[[math.ceil(m/2-1), m-2], math.ceil((m-2)/2)][0] is greater than block.u_a.at_day(1) + $0.03, then we need to buy 5000 options today and sell them tomorrow;
if solution[[math.ceil(m/2-1), m-2], math.ceil((m-2)/2)][1] is greater than block.u_a.at_day(2) + $0.03, then we need to buy 5000 options today and sell them the day after tomorrow.

ThomasBucaioni/IllPosedBlackScholesEquation