Binomial Pricer

The package offers the ability to price European and American options as well as futures contracts with a binomial tree. In the current version, only recombining trees are supported.

Option Pricing

Option pricing is carried out with the base class BinomialTreeOption

BinomialTreeOption(strike,
                   maturity,
                   initial_price=None,
                   price_tree=None,
                   steps=2,
                   probs=[None, None],
                   price_changes=[None, None],
                   tree_method='multiply',
                   int_rate=0.05,
                   int_rates_tree=None,
                   volatility=0,
                   dividents=0,
                   is_put=False,
                   is_american=False)           

At initialisation, the class has to be provided with:

1. The strike price and the maturity of the option.
2. Price tree: The recombining price tree for the underlying option can be specified in different ways. One way is to provide the price_tree directly. The other ways, are to provide an initial_price, along with the probabilities probs to transition to the [up-state, down-state] or to provide the price_changes for these transitions. Another parameter that has to be specified in this case is the tree_method, ='multiply' if at each time steps we multiply the current price with the price_changes and ='add' if we add them.
3. Interest: The interest rate at each node of the tree can be specified again with eitther of the two ways; by providint a constant int_rate, or specifiying the int_rates_tree directly.
4. If the option is_put and if it is_american.

Examples

More examples can be found in the tests/ directory.

Assume we have a stock with current price $105, and according to our model, at each step its value either increases by a factor of 1.2 or falls by a factor of 0.8 (with risk neutral probabilities). We want to price a European and an American put option with strike price $105 and maturity 2 years with 2 steps. The interest rate is constant and equal to 0.05.

import binompricer as bp
eu_put_option = bp.BinomialTreeOption(initial_price=100,
                                      strike=105,
                                      int_rate=0.05,
                                      maturity=2,
                                      steps=2,
                                      price_changes=[1.2, 0.8],
                                      tree_method='multiply',
                                      is_put=True,
                                      is_american=False)
eu_put_price = eu_put_option.price()
print("European 105-Put:", eu_put_price)

am_put_option = bp.BinomialTreeOption(initial_price=100,
                                      strike=105,
                                      int_rate=0.05,
                                      maturity=2,
                                      steps=2,
                                      price_changes=[1.2, 0.8],
                                      tree_method='multiply',
                                      is_put=True,
                                      is_american=True)
am_put_price = am_put_option.price()
print("American 105-put:", am_put_price)

European 105-Put: 8.933090552106973
American 105-put: 10.74429651994205