We present and test here several pricing formulas for target volatility options (TVO) assuming a lognormal fractional SABR (fSABR) model, having the stochastic volatility driven by a fractional Brownian motion (fBM). The formulas were developed and proved in the paper Alos et al. (2018) available on arXiv.
The files given in this repository are organized as follows:
| File | Description |
|---|---|
| utils.py | Utility functions needed to implement the lognormal fSABR process |
| fSABR.py | Class implementing the lognormal fSABR process |
| fSABR_test.py | Generate paths for fBM and fSABR process; check statistical properties of fBMs |
| tvo_pricing.py | TVO pricing via 3 methods: Monte Carlo and 2 analytic approximations |
| tvo_pricingSensitivity.py | TVO pricing formulae analysis and sensitivity to parameter variations |
| tvo_pricingSensitivityPlots.py | Plotting the sensitivities computed in tvo_pricingSensitivity.py |
| tvo_pricingNotebook.ipynb | Example Jupyter notebook which demonstrates usage of the code |
The code was tested with Python 3.6.3 (Anaconda custom on 64-bit) on a macOS X Yosemite (version 10.10.5) with processor 2 x 2.4 GHz 6-Core Intel Xeon.