OptiCalc: An intuitive and versatile options library

Overview

OptiCalc or options_calculator is a Python library designed to provide the user with a high-level and intuitive API for option pricing, greeks calculation, implied volatility calculation and more.

The core idea behind OptiCalc is to allow for complex calculations with a simple interface, filling the gap between simple End-user developed applications (EUDAs) and more advanced libraries/modules such as QuantLib. OptiCalc is not necessarily intended for speed or low-level complexity. For that, QuantLib is much more suitable.

Table of Contents

• Getting started with OptiCalc
• Features
• License
• Dependencies
• Roadmap

Getting started with OptiCalc

OptiCalc is available on PyPI and can be installed via

pip install options_calculator

Features

High-level Option Classes

Currently 4 option classes (EuropeanOption, AmericanOption, BermudaOption and Option) are available for use.

These option classes offer flexibility with their attributes, from simple, minimal inputs for quick calculations to more complex ones:

import options_calculator as op

# Minimal inputs
new_european_option = op.EuropeanOption(s = 100,
                                        k = 110,
                                        t = 0.10,
                                        r = 0.04,
                                        q = 0.00,
                                        sigma = 0.20,
                                        option_type = op.OptionType.Call)

# All possible inputs used
new_american_option = op.Option(s = 200,
                                k = 150,
                                t = 0.25,
                                r = 0.035,
                                q = 0.05,
                                sigma = 0.15,
                                option_type = "put",
                                exercise_style = op.ExerciseStyle.American,
                                b = None,
                                rf = 0.02,
                                premium = 5.5,
                                transaction_costs = 0.233,
                                underlying_type = op.Underlying.FX,
                                direction = "long",
                                underlying_contracts = 100)

Dynamic input

Assigning values to an option's attributes is also handled internally in a dynamic way, which allows for ease of use and personal preference when changing or assigning values.

import options_calculator as op

option = op.Option(...)

option.option_type = op.OptionType.Call
print(option.option_type)  # Output: op.OptionType.Call

option.option_type = "put"
print(option.option_type)  # Output: op.OptionType.Put

option.option_type = "Call"
print(option.option_type)  # Output: op.OptionType.Call

option.exercise_style = "european"
print(option.exercise_style)  # Output: op.ExerciseStyle.European

option.exercise_style = "BERMUDA"
print(option.exercise_style)  # Output: op.ExerciseStyle.Bermuda

option.underlying_type = op.Underlying.FX
print(option.underlying_type)  # Output: op.Underlying.FX

option.direction = "lOnG"
print(option.direction)  # Output: op.Direction.Long

The cost-of-carry logic

OptiCalc includes flexible handling of the option's cost of carry factor b. The cost of carry can either be defined when initializing a Option-type object or left to default to None. In that case, OptiCalc will try to infer b by looking at the option's underlying, where b will be set in the following manner:

Future:         b = 0
FX:             b = r - rf
Stock Index:    b = r - q
Bond:           b = r - q
Commodity:      b = r - q
Swap:           b = r - q
Not defined:    b = r - q

import options_calculator as op

underlying_price = 80
strike = 65
time_to_expiry = 0.333
risk_free_rate = 0.04
dividends = 0.01
volatility = 0.20
option_type = op.OptionType.Put
# b not defined!

new_option = op.EuropeanOption(underlying_price, strike, time_to_expiry,
                               risk_free_rate, dividends, volatility, option_type)

Since b is not explicitly defined when initializing the object, currently b = None. Given that, OptiCalc will autocalculate b. Since the underlying type is not defined, OptiCalc defaults to b = r - q.

print(new_option.b)  # Output: 0.03

Should the user want to, one can also modify b by simply assigning a new value to b. This will assign b a custom value which will means in future calls, no autocalculation based on the underlying will take place. This new value can simply be removed by calling the property reset_b which will result in b simply falling back to appropriate value based on the underlying or r - q in the default case.

new_option.b = 0.05
print(new_option.b)  # Output after modification: 0.05

new_option.reset_b
print(new_option.b) # Output: 0.03

new_option.underlying_type = op.Underlying.Future
new_option.reset_b
print(new_option.b) # Output: 0.00

Pricers

As of now, OptiCalc offers 5 different pricing classes, with 15 pricing methods available for european-style options, 12 for american-style options and 8 for bermuda-style options.

• Black Scholes (European options)

  • Black-Scholes
  • Black-Scholes-Merton
  • Black-76
  • Garman Kohlhagen
  • Adaptive Black-Scholes

• Binomial Trees (European, Bermuda and American options)

  • Cox-Ross-Rubinstein
  • Cox-Ross-Rubinstein with drift
  • Rendleman-Bartter
  • Leisen-Reimer
  • Jarrow-Rudd
  • Jarrow-Rudd with risk neutrality
  • Tian
  • Universal binomial tree

• Bjerksund-Stensland (American options)

  • Bjerksund-Stensland 1993 model
  • Bjerksund-Stensland 2002 model
  • Combined Bjerksund-Stensland 1993 and 2002 model

• Barone-Adesi and Whaley (American options)

  • Barone-Adesi and Whaley model

• Bachelier (European options)

  • Classic Bachelier model
  • Modified Bachelier model

License

OptiCalc is released under a MIT License

Dependencies

• SciPy: Adds statistical and probability functions like distributions.
• NumPy: Adds support for vectorized operations and the functions to process these.
• Matplotlib: Allows for visualization of greeks and option payoffs.

Roadmap

As OptiCalc is still under development, many features are still work-in progress and will be implemented in a similar order following the outline below:

• New pricing modules
  • Longstaff-Schwartz
  • Heston
  • Merton Jump Diffusion
  • Variance Gamma
  • Trinomial Trees
  • Monte Carlo
• Greeks support for american options
• Implied volatility
• Testing
• Expanded Documentation
• Extend support for exotic options (Asian, Barrier, Basket...)
• Global settings class for constants etc.
• Expand Plotting (Payoff graphs, Greeks)
• OptionStrategy class (Allows for the combination of several options)
  • Aggregate greeks
• Fully vectorized option classes (Option chains)