Saef, Danial; Wang, Yuanrong; Aste, Tomaso 07/09/2022
This library serves as a companion to the publication “Regime-based Implied Stochastic Volatility Model for Crypto Option Pricing”. However it can also be used independently for clustering high dimensional datasets and fitting an implied stochastic volatility model.
The increasing adoption of Digital Assets (DAs), such as Bitcoin (BTC), rises the need for accurate option pricing models. Yet, existing methodologies fail to cope with the volatile nature of the emerging DAs. Many models have been proposed to address the unorthodox market dynamics and frequent disruptions in the microstructure caused by the non-stationarity, and peculiar statistics, in DA markets. However, they are either prone to the curse of dimensionality, as additional complexity is required to employ traditional theories, or they overfit historical patterns that may never repeat.
Instead, we leverage recent advances in market regime (MR) clustering with the Implied Stochastic Volatility Model (ISVM). Time-regime clustering is a temporal clustering method, that clusters the historic evolution of a market into different volatility periods accounting for non-stationarity. ISVM can incorporate investor expectations in each of the sentiment-driven periods by using implied volatility (IV) data.
In this publication, we applied this integrated time-regime clustering and ISVM method (termed MR-ISVM) to high-frequency data on BTC options at the popular trading platform Deribit. We demonstrate that MR-ISVM contributes to overcome the burden of complex adaption to jumps in higher order characteristics of option pricing models. This allows us to price the market based on the expectations of its participants in an adaptive fashion.
For the exact methodology we refer to the methodology section of this paper, as well as Massara and Aste (2019), Procacci and Aste (2019), Wang and Aste (2022) for ICC, as well as Aït-Sahalia, Li, and Li (2021) for the ISVM methodology. Similar implementations can be found in those original works, however not for the MR-ISVM approach.
The usage is pretty simple. First, install the package with devtools.
library(devtools)
install_github("YalDan/icc.isvm")
library(icc.isvm)Now we can just load a suitable dataset and run the fit_ICC_ISVM
function. Note that as of now, the bootstrapping estimation of ISVM
requires the function mclapply from the parallel package. This
unfortunately won’t work on Windows machines. A Windows friendly
implementation is however planned in the future, as well as the option
to deactivate parallel computing. ICC can also be calculated in parallel
setting parallel_ICC = TRUE, however this is still experimental and it
is recommended to leave it at default. Inside the function
fit_ICC_ISVM is also a minimalistic example on how to run ICC and ISVM
individually.
DT_BTC_deribit_sample <- fread("DT_sample.csv")
ICC_ISVM_list_K2 <- fit_ICC_ISVM(DT_full = DT_BTC_deribit_sample,
last_date = as.Date("2022-01-28"),
K = 2,
gamma = 0.5)If needed, the resulting plots from the model can be saved by using the make_plots function.
make_plots(ICC_ISVM_list_K2, SAVE_PLOTS = FALSE)Aït-Sahalia, Yacine, Chenxu Li, and Chen Xu Li. 2021. “Implied Stochastic Volatility Models.” The Review of Financial Studies 34 (1): 394–450. https://doi.org/10.1093/rfs/hhaa041.
Massara, Guido Previde, and Tomaso Aste. 2019. “Learning Clique Forests,” May. https://doi.org/10.48550/arXiv.1905.02266.
Procacci, Pier Francesco, and Tomaso Aste. 2019. “Forecasting Market States.” Quantitative Finance 19 (9): 1491–98. https://doi.org/10.1080/14697688.2019.1622313.
Wang, Yuanrong, and Tomaso Aste. 2022. “Dynamic Portfolio Optimization with Inverse Covariance Clustering.” 2112.15499. arXiv.org. https://doi.org/10.48550/arXiv.2112.15499.