0be4c8a2d7
* Added variables for binom function * Finished binom function * Updated .ipynb handling * James updates * Expanded definitions * Expanded description
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usage: binom [-s STRIKE] [-p] [-e] [-E] [-P] [-v VOLATILITY] [-h]
Shows the value of an option using binomial option pricing. Can also show raw data and provide a graph with predicted underlying asset ending values. The binomial options model calculates how big an up step or down step in the next time period will likely be. Then it creates a tree doing this at each period. The end results of this is a tree with possible asset values at each "step". For our calculations we use a day as our "step" time period. We then take all of the expected values at the finishing date and use this to begin a tree of option values at each step. The ending results is the value of the option today.
The up step is calculated by taking e to the power of volatility times the square root of the change in time during the step. This is the percentage we expect the stock to increase if there is an upward movement. The down step is the inverse of the up step. The probability of the up step is calculated by taking e to the power of the risk free rate minus the dividend yield. This is multiplied by the change in time for the step and then subtracted by the expected downward movement. This number is then divided by the up step subtracted by then down step. The probability of a downward step is just one minus the probability of an upward step.
Formulas: up_step = e ^ (volatility * (delta_t ^ (1 / 2))) down_step = 1 / up_step
prob_up = (e ^ ((risk_free - div_yield) * delta_t) - down_step) / (up_step - down_step) prob_down = 1 - prob_up
optional arguments:
-s STRIKE, --strike STRIKE
strike price for the option (default: 0)
-p, --put value the option as a put (default: False)
-e, --european value the option as a European option (default: False)
--export export the binomial trees (default: False)
-P, --plot plots the expected underlying asset ending prices (default: False)
-v, --volatility sets the volatility for the underlying asset(default: None)
-h, --help show this help message (default: False)