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Added trinomial tree #9

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12 changes: 11 additions & 1 deletion development_testing.py
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Original file line number Diff line number Diff line change
Expand Up @@ -128,6 +128,16 @@
# print(eqOption_BSM_test_pricer.risk_parameters_num())
# print(eqOption_BSM_test_pricer.risk_parameters())

# #
# """EqOption using Trinomial"""
# eqOption_BSM_test = qbdp.EqOption(option_type='Call', strike=100, expiry_date='20180630', expiry_type='American')
# eqOption_BSM_test_pricer = eqOption_BSM_test.engine(model="Trinomial", spot0=110, pricing_date='20180531', volatility=.25,
# rf_rate=.05, div_list=div_list, yield_div=0.01, seed=12)
#
# print(eqOption_BSM_test_pricer.valuation())
# print(eqOption_BSM_test_pricer.risk_parameters_num())
# print(eqOption_BSM_test_pricer.risk_parameters())

# """FutOption using Binomial"""
# eqOption_BSM_test = qbdp.FutOption(option_type='Call', strike=100, expiry_date='20180630', expiry_type='American')
# eqOption_BSM_test_pricer = eqOption_BSM_test.engine(model="Binomial", fwd0=110, pricing_date='20180531', volatility=.25,
Expand Down Expand Up @@ -225,4 +235,4 @@
print(delta)
delta.show()

"""
"""
21 changes: 11 additions & 10 deletions quantsbin/derivativepricing/namesnmapper.py
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Expand Up @@ -24,7 +24,7 @@ class PricingModel(Enum):
MC_GBM = "MC_GBM"
MC_GBM_LSM = "MC_GBM_LSM"
BINOMIAL = "Binomial"

TRINOMIAL = "Trinomial"

class UnderlyingParameters(Enum):
SPOT = "spot0"
Expand Down Expand Up @@ -72,17 +72,17 @@ class DivType(Enum):

OBJECT_MODEL = {
UdlType.STOCK.value: {ExpiryType.EUROPEAN.value: [PricingModel.BLACKSCHOLESMERTON.value, PricingModel.MC_GBM.value
, PricingModel.BINOMIAL.value],
ExpiryType.AMERICAN.value: [PricingModel.MC_GBM.value, PricingModel.BINOMIAL.value]}
, PricingModel.BINOMIAL.value, PricingModel.TRINOMIAL.value],
ExpiryType.AMERICAN.value: [PricingModel.MC_GBM.value, PricingModel.BINOMIAL.value, PricingModel.TRINOMIAL.value]}
, UdlType.FUTURES.value: {ExpiryType.EUROPEAN.value: [PricingModel.BLACK76.value, PricingModel.MC_GBM.value
, PricingModel.BINOMIAL.value],
ExpiryType.AMERICAN.value: [PricingModel.MC_GBM.value, PricingModel.BINOMIAL.value]}
, PricingModel.BINOMIAL.value, PricingModel.TRINOMIAL.value],
ExpiryType.AMERICAN.value: [PricingModel.MC_GBM.value, PricingModel.BINOMIAL.value, PricingModel.TRINOMIAL.value]}
, UdlType.FX.value: {ExpiryType.EUROPEAN.value: [PricingModel.GK.value, PricingModel.MC_GBM.value
, PricingModel.BINOMIAL.value],
ExpiryType.AMERICAN.value: [PricingModel.MC_GBM.value, PricingModel.BINOMIAL.value]}
, PricingModel.BINOMIAL.value, PricingModel.TRINOMIAL.value],
ExpiryType.AMERICAN.value: [PricingModel.MC_GBM.value, PricingModel.BINOMIAL.value, PricingModel.TRINOMIAL.value]}
, UdlType.COMMODITY.value: {ExpiryType.EUROPEAN.value: [PricingModel.GK.value, PricingModel.MC_GBM.value
, PricingModel.BINOMIAL.value],
ExpiryType.AMERICAN.value: [PricingModel.MC_GBM.value, PricingModel.BINOMIAL.value]}
, PricingModel.BINOMIAL.value, PricingModel.TRINOMIAL.value],
ExpiryType.AMERICAN.value: [PricingModel.MC_GBM.value, PricingModel.BINOMIAL.value, PricingModel.TRINOMIAL.value]}
}

DEFAULT_MODEL = {
Expand Down Expand Up @@ -115,5 +115,6 @@ class DivType(Enum):
PricingModel.BLACK76.value: pm.B76,
PricingModel.GK.value: pm.GK,
PricingModel.MC_GBM.value: pm.MonteCarloGBM,
PricingModel.BINOMIAL.value: pm.BinomialModel
PricingModel.BINOMIAL.value: pm.BinomialModel,
PricingModel.TRINOMIAL.value: pm.TrinomialModel
}
106 changes: 106 additions & 0 deletions quantsbin/derivativepricing/pricingmodels.py
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Original file line number Diff line number Diff line change
Expand Up @@ -3,6 +3,9 @@

"""

# ExtraLine1
# ExtraLine2
# ExtraLine3
from abc import ABCMeta, abstractmethod
from datetime import datetime as dt
from math import log, sqrt
Expand Down Expand Up @@ -476,4 +479,107 @@ def valuation(self):
def risk_parameters(self):
pass

class TrinomialModel(Model):
"""
This is the generalised Trinomial model used for valuation calculation for both European and American type
Args required:
instrument = Instrument parameters mapped from instrument module
spot0 = (Float) e.g. 110.0
rf_rate = (Float < 1) e.g. 0.2
cnv_yield = (Float < 1) e.g. 0.3
cost_yield = (Float < 1) e.g. 0.2
volatility = (Float < 1) e.g. 0.25
pricing_date = (Date in string format "YYYYMMDD") e.g. 10 Dec 2018 as "20181210"
no_of_steps = (Integer). Number of steps (nodes) for the premium calculation e.g. 100
div_list = (List). list of tuples with Ex-Dates and Dividend amounts. e.g. [('20180625',0.2),('20180727',0.6)]

"""

def __init__(self, instrument, spot0=None, rf_rate=0, cnv_yield=0, cost_yield=0,
volatility=None, pricing_date=None, no_of_steps=None, div_list=None, **kwargs):
self.instrument = instrument
self.spot0 = spot0 or 0.0001
self.rf_rate = rf_rate or 0
self.cnv_yield = cnv_yield or 0
self.cost_yield = cost_yield or 0
self.volatility = volatility or 0.10
self._pricing_date = dt.strptime(pricing_date, '%Y%m%d')
self.no_of_steps = no_of_steps or 100
self.div_list = div_list
self.cache_node = {}

@property
def drift(self):
return self.rf_rate + self.cost_yield - self._cnv_yield

@property
def div_processed(self):
return dividend_processor(self.div_list, self._pricing_date, self.instrument.expiry_date)

@property
def spot_update(self):
return self.spot0 - pv_div(self.div_processed, 0, self.rf_rate)

@property
def t_delta(self):
return self.maturity/self.no_of_steps

@property
def up_mult(self):
return e**(self.volatility*((2 * self.t_delta) ** 0.5))

@property
def up_prob(self):
return (1/6 + (self.drift - 0.5 * self.volatility**2 ) * (self.t_delta/(12*self.volatility**2))**0.5 )

@property
def dn_prob(self):
return (1/6 - (self.drift - 0.5 * self.volatility**2 ) * (self.t_delta/(12*self.volatility**2))**0.5 )

@property
def md_prob(self):
return 2/3

@property
def step_discount_fact(self):
return e**(-1*self.rf_rate * self.t_delta)

def node_value_store(self, pv, intrinsic_value):
if self.instrument.expiry_type == ExpiryType.AMERICAN.value:
return max(pv, intrinsic_value)
else:
return pv

def intrinsic_value(self, _spot):
return max(self.option_flag * (_spot - self.instrument.strike), 0.0)

def calc_spot(self, step_no, no_up):
return self.spot_update * (self.up_mult**(1*no_up - 0*step_no)) + \
pv_div(self.div_processed, self.t_delta * step_no, self.rf_rate)

def node_value(self, step_no, no_up):
cache_node_key = (step_no, no_up)
if cache_node_key in self.cache_node:
return self.cache_node[cache_node_key]
else:
_spot = self.calc_spot(step_no, no_up)
_intrinsic_value = self.intrinsic_value(_spot)

if step_no >= self.no_of_steps:
return _intrinsic_value
else:
_pv = ((self.up_prob*self.node_value(step_no+1, no_up+1)) +
(self.md_prob*self.node_value(step_no+1, no_up)) +
(self.dn_prob*self.node_value(step_no+1, no_up-1))
)*self.step_discount_fact
_node_value = self.node_value_store(_pv,_intrinsic_value)
self.cache_node[cache_node_key] = _node_value
return self.cache_node[cache_node_key]

def valuation(self):
return self.node_value(0, 0)

def risk_parameters(self):
pass