Package: arbitragerepair
arbitragerepairPython modules and jupyter notebook examples for the paperDetect and Repair
Arbitrage in Price Data of Traded Options.Repair option price data -- remove arbitrageFor a finite collection of call option prices written on the same underlying
asset, there are six types of constraints that ensure their prices to be
statically arbitrage-free. Given violation of the arbitrage constraints, we
repair the price data in a fast, model-independent way to remove all arbitrages.Some examples of arbitrage repair are shown as below:An arbitrage-free normalised call price surfaceshould satisfy some shape constraints. Assuming smooth surface function,
then these shape constraints arePositivity:Monotonicity:,Convexity:CodeInstallationIt is recommended to create a new virtual environment and install from pypi.pip install arbitragerepairRequirements:Python >= 3.8andCVXOPT >= 1.3.0.UsageWhile an example can be found inthis jupyter notebook,
the usage of this code consists of the following steps.0.Import packagesfrom arbitragerepair import constraints, repair1.Normalise strikes and call pricesThe inputs are four 1Dnumpy.arrayobjectsT, K, C, F, which should be of the same length, representing
time-to-expiries, strike prices, option prices and forward prices.normaliser = constraints.Normalise()
normaliser.fit(T, K, C, F)
T1, K1, C1 = normaliser.transform(T, K, C)2.Construct arbitrage constraints and detect violationmat_A, vec_b, _, _ = constraints.detect(T1, K1, C1, verbose=True)Settingverbose=True, an arbitrage detection report will be shown. An example
is shown below:Number of violations to non-negative outright price:                   0/13
Number of violations to non-negative and unit-bounded vertical spread: 0/130
Number of violations to non-negative butterfly spread:                 0/104
Number of violations to non-negative calendar (horizontal) spread:     0/0
Number of violations to non-negative calendar vertical spread:         9/513
Number of violations to non-negative calendar butterfly spread:        126/30703.Repair arbitrageRepair using the-norm
objective:epsilon = repair.l1(mat_A, vec_b, C1)Repair using the-BA
objective (where bid-ask spreads data need to be supplied):epsilon = repair.l1ba(mat_A, vec_b, C1, spread)4.De-normaliseK0, C0 = normaliser.inverse_transform(K1, C1 + epsilon)Why is repairing arbitrage in price data important?Frequent presence of arbitrage in historical price dataWe collect daily close (bid, ask and mid) prices from 1st November, 2007 to 31st May,
2018 for OTC FX options from Bloomberg. We count violations of arbitrage constraints
in raw daily close mid-prices over time for some major currencies and emerging market
(EM) currencies.Repairing arbitrage can improve robustness of model calibrationWe verify that our repair method improves model calibration with more robust parameter
estimates and smaller calibration error.Experiment designResultsHow do our algorithm and code perform in practice?All of the following studies were carried out on a quadcore Intel Core i7-8650U CPU
with 32GB RAM. All LPs are solved using the GLPK (GNU Linear Programming Kit) solver
wrapped by theCVXOPTPython package.The formation and disappearance of executable arbitrageWe can use the our method on order book data for identifying executable arbitrage. An
example is given below. We collect the order book data for all E-mini S&P 500 monthly
European call options from 12:00 ET to 16:10 ET on 12th June, 2020. There is a large
spike of number of arbitrages at around 15:52 ET, a few minutes before the close of
the S&P 500 index market at 16:00 ET. This spike coincided with rallies in the futures
market, while the IV maintained its relatively low level.The formation and disappearance of intra-day executable arbitrage opportunities in the
E-mini S&P 500 monthly European call option market on 12th June, 2020.Citation@misc{arbitragerepair2020,
   author = {Samuel N. Cohen and Christoph Reisinger and Sheng Wang},  
   title = {arbitragerepair},
   publisher = {GitHub},
   journal = {GitHub repository},
   year = {2020},
   howpublished = {\url{https://github.com/vicaws/arbitragerepair}},
   note = {DOI: 10.5281/zenodo.5338299}
}