pyfe / pyfeng

Python Financial ENGineering (PyFENG package in PyPI.org)

PyFENG: [Py]thon [F]inancial [ENG]ineering

PyFENG provides an implementation of the standard financial engineering models for derivative pricing.

Implemented Models

• Black-Scholes-Merton (BSM) and displaced BSM models:
  • Analytic option price, Greeks, and implied volatility.
• Bachelier (Normal) model
  • Analytic option price, Greeks, and implied volatility.
• Constant-elasticity-of-variance (CEV) model
  • Analytic option price, Greeks, and implied volatility.
• Stochastic-alpha-beta-rho (SABR) model
  • Hagan's BSM vol approximation.
  • Choi & Wu's CEV vol approximation.
  • Analytic integral for the normal SABR.
  • Closed-form MC simulation for the normal SABR.
• Hyperbolic normal stochastic volatility (NSVh) model
  • Analytic option pricing.
• Heston model
  • FFT option pricing.
  • Almost exact MC simulation by Glasserman & Kim and Choi & Kwok.
• Schobel-Zhu (OUSV) model
  • FFT option pricing.
  • Almost exact MC simulation by Choi
• Rough volatility models
  • Rough Heston MC by Ma & Wu

About the Package

• Uses numpy arrays as basic datatype so computations are naturally vectorized.
• Purely Python without C/C++ extensisons.
• Implemented with Python class.
• Intended for academic use. By providing reference models, it saves researchers' time. See PyFENG for Papers in Related Projects below.

Installation

pip install pyfeng

For upgrade,

pip install pyfeng --upgrade

Code Snippets

In [1]:

import numpy as np
import pyfeng as pf
m = pf.Bsm(sigma=0.2, intr=0.05, divr=0.1)
m.price(strike=np.arange(80, 121, 10), spot=100, texp=1.2)

Out [1]:

array([15.71361973,  9.69250803,  5.52948546,  2.94558338,  1.48139131])

In [2]:

sigma = np.array([[0.2], [0.5]])
m = pf.Bsm(sigma, intr=0.05, divr=0.1) # sigma in axis=0
m.price(strike=[90, 95, 100], spot=100, texp=1.2, cp=[-1,1,1])

Out [2]:

array([[ 5.75927238,  7.38869609,  5.52948546],
       [16.812035  , 18.83878533, 17.10541288]])

Author

• Prof. Jaehyuk Choi (Peking University HSBC Business School). Email: [email protected]

Related Projects

• Commercial versions (implemented and optimized in C/C++) for some models are available. Email the author at [email protected].
• PyFENG for Papers is a collection of Jupyter notebooks that reproduce the results of financial engineering research papers using PyFENG.
• FER: Financial Engineering in R developed by the same author. Not all models in PyFENG are implemented in FER. FER is a subset of PyFENG.

pyfeng's Issues

Implement options on realized variance

• Drimus GG (2012) Options on realized variance by transform methods: a non-affine stochastic volatility model. Quantitative Finance 12:1679–1694. https://doi.org/10.1080/14697688.2011.565789

Quadrature from moments

• quadpypackage
  • Example
• Golub GH, Meurant GA (2010) Matrices, moments, and quadrature with applications. Princeton University Press, Princeton, N.J

Make BsmNdMc and OptMaABC to handle a single asset case.

Option model based on inverse Gaussian

Abate & Whitt algorithm

Implement the Abate & Whitt's (1992?) algorithm for inverting Laplace transform

`BsmDisp` bug

The disp() function should take forward, not spot.

Oosterlee's COS method for European Option

• Fang F, Oosterlee C (2008) A Novel Pricing Method for European Options Based on Fourier-Cosine Series Expansions. SIAM J Sci Comput 31:826–848. https://doi.org/10.1137/080718061

• Oosterlee CW, Grzelak LA (2019) Mathematical modeling and computation in finance: with exercises and python and matlab computer codes, 1st edn. World Scientific Publishing Co. Pte. Ltd, Hackensack

https://github.com/LechGrzelak/QuantFinanceBook

OusvIft is not accurate.

The current docstring in OusvIft shows the exact values reported in Li & Wu (2019) Table 2 and 3. But the actual output is slightly different. We need to improve the implementation.

        >>> import pyfeng as pf
        >>> model = pf.OusvIft(0.2, mr=4, vov=0.1, rho=-0.7, intr=0.09531)
        >>> model.price(100, 100, texp=np.array([1, 5, 10]))
        array([13.21493, 40.79773, 62.76312])
        >>> model = pf.OusvIft(0.25, mr=8, vov=0.3, rho=-0.6, intr=0.09531)
        >>> model.price(np.array([90, 100, 110]), 100, texp=1)
        array([21.41873, 15.16798, 10.17448])

Actual results:

array([13.21341236, 40.78514465, 62.67427669])
array([21.41624282, 15.16575302, 10.17145969])

Numpy asscalar deprecation

PyFENG/pyfeng/bsm.py

Line 327 in 1ee5f9e

_sigma = np.asscalar(_sigma)

The referenced call to np.asscalar needs to be changed to _sigma.item(). np.asscalar was deprecated.

https://numpy.org/doc/1.22/reference/generated/numpy.asscalar.html

Improve moments-related methods

• Change moments_vsk to moments_mvsk to show the mean (normalization)
• Vectorize moments for Asian/Basket options

SabrMcExactCai2017

Fix error after noramalization

Improve InvGam model

• Add vol_smile
• Change name to InvGam

Implement approximate IV for the Heston and 3/2 models

Medvedev A, Scaillet O (2007) Approximation and Calibration of Short-Term Implied Volatilities Under Jump-Diffusion Stochastic Volatility. The Review of Financial Studies 20:427–459. https://doi.org/10.1093/rfs/hhl013

Drimus GG (2012) Options on realized variance by transform methods: a non-affine stochastic volatility model. Quantitative Finance 12:1679–1694. https://doi.org/10.1080/14697688.2011.565789

Heston and 3/2 models

Asian option creator to Basket option class

Asian option is a special kind of basket option.
Provide an alternative creator for the basket option classes

Better to fix random number seed (`rn_seed`) by default?

Currently rn_seed=None by default.
Perhaps it's better to fix as rn_seed=123456?

implied volatility problem

It seems that both impvol and impvol_naive return nan:

m = pf.Bsm(sigma=0.5, intr=0.05, divr=0.1)
print(m.impvol(100, 80, 19.4, 0.1, 1))

nan

Add function cache / memoization

Function / Class cache has been implemented since Py 3.9

• https://docs.python.org/dev/library/functools.html#functools.cache

• https://stackoverflow.com/questions/815110/is-there-a-decorator-to-simply-cache-function-return-values

Mgf2Mom improvement

• Vectorize. MGF can return vectors
• Intermediate results should use class variables