arXiv subjects

Sebastian Jaimungal

Publications and source records attributed to Sebastian Jaimungal.

67 records · Page 4Linked to original sources

arXiv2018

Trading algorithms with learning in latent alpha models

Alpha signals for statistical arbitrage strategies are often driven by latent factors. This paper analyses how to optimally trade with latent factors that cause prices to jump and diffuse. Moreover, we account for the effect of the trader's actions on quoted prices and the prices they receive from trading. Under fairly general assumptions, we demonstrate how the trader can learn the posterior distribution over the latent states, and explicitly solve the latent optimal trading problem. We provide a verification theorem, and a methodology for calibrating the model by deriving a variation of the expectation-maximization algorithm. To illustrate the efficacy of the optimal strategy, we demonstrate its performance through simulations and compare it to strategies which ignore learning in the latent factors. We also provide calibration results for a particular model using Intel Corporation stock as an example.

q-fin.MF↗

arXiv2018

Foreign Exchange Markets with Last Look

We examine the Foreign Exchange (FX) spot price spreads with and without Last Look on the transaction. We assume that brokers are risk-neutral and they quote spreads so that losses to latency arbitrageurs (LAs) are recovered from other traders in the FX market. These losses are reduced if the broker can reject, ex-post, loss-making trades by enforcing the Last Look option which is a feature of some trading venues in FX markets. For a given rejection threshold the risk-neutral broker quotes a spread to the market so that her expected profits are zero. When there is only one venue, we find that the Last Look option reduces quoted spreads. If there are two venues we show that the market reaches an equilibrium where traders have no incentive to migrate. The equilibrium can be reached with both venues coexisting, or with only one venue surviving. Moreover, when one venue enforces Last Look and the other one does not, counterintuitively, it may be the case that the Last Look venue quotes larger spreads.

q-fin.TR↗

arXiv2012

Spectral Decomposition of Option Prices in Fast Mean-Reverting Stochastic Volatility Models

Using spectral decomposition techniques and singular perturbation theory, we develop a systematic method to approximate the prices of a variety of options in a fast mean-reverting stochastic volatility setting. Four examples are provided in order to demonstrate the versatility of our method. These include: European options, up-and-out options, double-barrier knock-out options, and options which pay a rebate upon hitting a boundary. For European options, our method is shown to produce option price approximations which are equivalent to those developed in [5]. [5] Jean-Pierre Fouque, George Papanicolaou, and Sircar Ronnie. Derivatives in Financial Markets with Stochas- tic Volatility. Cambridge University Press, 2000.

q-fin.PR↗

arXiv2011

The Generalized Shiryaev's Problem and Skorohod Embedding

In this paper we consider a connection between the famous Skorohod embedding problem and the Shiryaev inverse problem for the first hitting time distribution of a Brownian motion: given a probability distribution, $F$, find a boundary such that the first hitting time distribution is $F$. By randomizing the initial state of the process we show that the inverse problem becomes analytically tractable. The randomization of the initial state allows us to significantly extend the class of target distributions in the case of a linear boundary and moreover allows us to establish connection with the Skorohod embedding problem.

math.PR↗

arXiv2009

Randomized First Passage Times

In this article we study a problem related to the first passage and inverse first passage time problems for Brownian motions originally formulated by Jackson, Kreinin and Zhang (2009). Specifically, define $τ_X = \inf\{t>0:W_t + X \le b(t) \}$ where $W_t$ is a standard Brownian motion, then given a boundary function $b:[0,\infty) \to \RR$ and a target measure $μ$ on $[0,\infty)$, we seek the random variable $X$ such that the law of $τ_X$ is given by $μ$. We characterize the solutions, prove uniqueness and existence and provide several key examples associated with the linear boundary.

math.PR↗

arXiv2009

Integral Equations and the First Passage Time of Brownian Motions

The first passage time problem for Brownian motions hitting a barrier has been extensively studied in the literature. In particular, many incarnations of integral equations which link the density of the hitting time to the equation for the barrier itself have appeared. Most interestingly, Peskir(2002b) demonstrates that a master integral equation can be used to generate a countable number of new equations via differentiation or integration by parts. In this article, we generalize Peskir's results and provide a more powerful unifying framework for generating integral equations through a new class of martingales. We obtain a continuum of Volterra type integral equations of the first kind and prove uniqueness for a subclass. Furthermore, through the integral equations, we demonstrate how certain functional transforms of the boundary affect the density function. Finally, we demonstrate a fundamental connection between the Volterra integral equations and a class of Fredholm integral equations.

math.PR↗

arXiv2007

Option Valuation using Fourier Space Time Stepping

It is well known that the Black-Scholes-Merton model suffers from several deficiencies. Jump-diffusion and Levy models have been widely used to partially alleviate some of the biases inherent in this classical model. Unfortunately, the resulting pricing problem requires solving a more difficult partial-integro differential equation (PIDE) and although several approaches for solving the PIDE have been suggested in the literature, none are entirely satisfactory. All treat the integral and diffusive terms asymmetrically and are difficult to extend to higher dimensions. We present a new, efficient algorithm, based on transform methods, which symmetrically treats the diffusive and integrals terms, is applicable to a wide class of path-dependent options (such as Bermudan, barrier, and shout options) and options on multiple assets, and naturally extends to regime-switching Levy models. We present a concise study of the precision and convergence properties of our algorithm for several classes of options and Levy models and demonstrate that the algorithm is second-order in space and first-order in time for path-dependent options.

cs.CE↗

arXiv2000

Coulomb Gas Representation of Low Energy QCD

A novel Coulomb gas (CG) description of low energy $QCD_4$, based on the dual transformation of the QCD effective chiral Lagrangian, is constructed. The CG is found to contain several species of charges, one of which is fractionally charged and can be interpreted as instanton-quarks. The creation operator which inserts a pseudo-particle in the CG picture is explicitly constructed and demonstrated to have a non-zero vacuum expectation value. The Wilson loop operator as well as the creation operator for the domain wall in the CG representation is also constructed.

hep-ph↗

arXiv1999

Phase transition in quantum gravity

A fundamental problem with attempting to quantize general relativity is its perturbative non-renormalizability. However, this fact does not rule out the possibility that non-perturbative effects can be computed, at least in some approximation. We outline a quantum field theory calculation, based on general relativity as the classical theory, which implies a phase transition in quantum gravity. The order parameters are composite fields derived from spacetime metric functions. These are massless below a critical energy scale and become massive above it. There is a corresponding breaking of classical symmetry.

gr-qc↗

arXiv1999

Monopoles and Coulomb Gas Representation of the QCD Effective Lagrangian

A novel Coulomb gas (CG) description of low energy QCD_4(N_c) is constructed. The construction is based on the dual transformation of the QCD effective Lagrangian. By considering a large gauge transformation, the charges of this statistical system are identified with magnetic monopoles which carry fractional charges of strength 1/N_c. Furthermore, the creation operator which inserts the magnetic charge in the CG picture is explicitly constructed and demonstrated to have a non-zero vacuum expectation value, indicating that confinement does occur. The Wilson loop operator as well as the creation operator for the domain wall in CG representation is also constructed. Additional support for the D-brane picture suggested by Witten is also found. Lastly, the relation of the CG picture with the instanton-quarks is also discussed.

hep-ph↗

arXiv1999

Topological Holography

We study a topological field theory in four dimensions on a manifold with boundary. A bulk-boundary interaction is introduced through a novel variational principle rather than explicitly. Through this scheme we find that the boundary values of the bulk fields act as external sources for the boundary theory. Furthermore, the full quantum states of the theory factorize into a single bulk state and an infinite number of boundary states labeled by loops on the spatial boundary. In this sense the theory is purely holographic. We show that this theory is dual to Chern-Simons theory with an external source. We also point out that the holographic hypothesis must be supplemented by additional assumptions in order to take into account bulk topological degrees freedom, since these are apriori invisible to local boundary fields.

hep-th↗

arXiv1998

Wilson Loops, Bianchi Constraints and Duality in Abelian Lattice Models

We introduce new modified Abelian lattice models, with inhomogeneous local interactions, in which a sum over topological sectors are included in the defining partition function. The dual models, on lattices with arbitrary topology, are constructed and they are found to contain sums over topological sectors, with modified groups, as in the original model. The role of the sum over sectors is illuminated by deriving the field-strength formulation of the models in an explicitly gauge-invariant manner. The field-strengths are found to satisfy, in addition to the usual local Bianchi constraints, global constraints. We demonstrate that the sum over sectors removes these global constraints and consequently softens the quantization condition on the global charges in the system. Duality is also used to construct mappings between the order and disorder variables in the theory and its dual. A consequence of the duality transformation is that correlators which wrap around non-trivial cycles of the lattice vanish identically. For particular dimensions this mapping allows an explicit expression for arbitrary correlators to be obtained.

hep-th↗

arXiv1998

T-Duality in Lattice Regularized Sigma Models

It is shown that when the underlying sigma model of bosonic string theory is written in terms of single-valued fields, which live in the covering space of the target space, Abelian T-duality survives lattice regularization of the world-sheet. The projection onto the target-space is implemented through a sum over cohomology, which bears resemblance to summing over topological sectors in Yang-Mills theories. In particular, the case of string theory on a circle is shown to be explicitly self-dual in the lattice regulated model and automatically forbids vortex excitations which would otherwise destroy the duality. For other target spaces a generalized notion of T-duality is observed in which the target space and the cohomology coefficient group are interchanged under duality. Specific examples show that the fundamental group of the target space may not be preserved in the T-dual theory. Generalized models which exhibit T-duality behaviour, with dynamical variables that live on the k-dimensional cells of (p+1)-dimensional world-volumes, are also constructed. These models correspond to gauge theories, and higher-dimensional analogues, in which one sums over various topological sectors of the theory.

hep-th↗