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• 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

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

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])

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

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

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

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

• 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

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

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

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

• Add vol_smile
• Change name to InvGam

Fix error after noramalization

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

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

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