20 research outputs found
Post trade allocation: how much are bunched orders costing your performance?
Individual trade orders are often bunched into a block order for processing
efficiency, where in post execution, they are allocated into individual
accounts. Since Regulators have not mandated any specific post trade allocation
practice or methodology, entities try to rigorously follow internal policies
and procedures to meet the minimum Regulatory ask of being procedurally fair
and equitable. However, as many have found over the years, there is no simple
solution for post trade allocation between accounts that results in a uniform
distribution of returns. Furthermore, in many instances, the divergences
between returns do not dissipate with more transactions, and tend to increase
in some cases. This paper is the first systematic treatment of trade allocation
risk. We shed light on the reasons for return divergence among accounts, and we
present a solution that supports uniform allocation of return irrespective of
number of accounts and trade sizes.Comment: 16 pages, 2 figures, 12 table
A fast method for pricing American options under the variance gamma model
We investigate methods for pricing American options under the variance gamma
model. The variance gamma process is a pure jump process which is constructed
by replacing the calendar time by the gamma time in a Brownian motion with
drift, which makes it a time-changed Brownian motion. In general, the finite
difference method and the simulation method can be used for pricing under this
model, but their speed is not satisfactory. So there is a need for fast but
accurate approximation methods. In the case of Black-Merton-Scholes model,
there are fast approximation methods, but they cannot be utilized for the
variance gamma model. We develop a new fast method inspired by the quadratic
approximation method, while reducing the error by making use of a machine
learning technique on pre-calculated quantities. We compare the performance of
our proposed method with those of the existing methods and show that this
method is efficient and accurate for practical use.Comment: 16 pages, 1 Figure, 4 Table
An unsupervised deep learning approach in solving partial integro-differential equations
We investigate solving partial integro-differential equations (PIDEs) using
unsupervised deep learning in this paper. To price options, assuming underlying
processes follow Levy processes, we require to solve PIDEs. In supervised deep
learning, pre-calculated labels are used to train neural networks to fit the
solution of the PIDE. In an unsupervised deep learning, neural networks are
employed as the solution, and the derivatives and the integrals in the PIDE are
calculated based on the neural network. By matching the PIDE and its boundary
conditions, the neural network gives an accurate solution of the PIDE. Once
trained, it would be fast for calculating options values as well as option
Greeks.Comment: 22 pages, 4 figure
The VIX index under scrutiny of machine learning techniques and neural networks
The CBOE Volatility Index, known by its ticker symbol VIX, is a popular
measure of the market's expected volatility on the SP 500 Index, calculated and
published by the Chicago Board Options Exchange (CBOE). It is also often
referred to as the fear index or the fear gauge. The current VIX index value
quotes the expected annualized change in the SP 500 index over the following 30
days, based on options-based theory and current options-market data. Despite
its theoretical foundation in option price theory, CBOE's Volatility Index is
prone to inadvertent and deliberate errors because it is weighted average of
out-of-the-money calls and puts which could be illiquid. Many claims of market
manipulation have been brought up against VIX in recent years.
This paper discusses several approaches to replicate the VIX index as well as
VIX futures by using a subset of relevant options as well as neural networks
that are trained to automatically learn the underlying formula. Using subset
selection approaches on top of the original CBOE methodology, as well as
building machine learning and neural network models including Random Forests,
Support Vector Machines, feed-forward neural networks, and long short-term
memory (LSTM) models, we will show that a small number of options is sufficient
to replicate the VIX index. Once we are able to actually replicate the VIX
using a small number of SP options we will be able to exploit potential
arbitrage opportunities between the VIX index and its underlying derivatives.
The results are supposed to help investors to better understand the options
market, and more importantly, to give guidance to the US regulators and CBOE
that have been investigating those manipulation claims for several years
Deep reinforcement learning on a multi-asset environment for trading
Financial trading has been widely analyzed for decades with market participants and academics always looking for advanced methods to improve trading performance. Deep reinforcement learning (DRL), a recently reinvigorated method with significant success in multiple domains, still has to show its benefit in the financial markets. We use a deep Q-network (DQN) to design long-short trading strategies for futures contracts. The state space consists of volatility-normalized daily returns, with buying or selling being the reinforcement learning action and the total reward defined as the cumulative profits from our actions. Our trading strategy is trained and tested both on real and simulated price series and we compare the results with an index benchmark. We analyze how training based on a combination of artificial data and actual price series can be successfully deployed in real markets. The trained reinforcement learning agent is applied to trading the E-mini S&P 500 continuous futures contract. Our results in this study are preliminary and need further improvement