# Luis A. SecoUniversity of Toronto | U of T

Luis A. Seco

Ph.D. Princeton University

## About

107

Publications

25,672

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1,206

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Introduction

Additional affiliations

January 2006 - present

July 1992 - present

September 1989 - July 1992

Education

September 1985 - June 1989

September 1983 - June 1985

September 1980 - June 1983

## Publications

Publications (107)

This paper develops an integrated framework to forecast the volatility of crude oil prices by considering the impacts of extreme events (structural breaks). The impacts of extreme events are vital to improving prediction accuracy. Aiming to demonstrate the crude oil price fluctuation and the impacts of external events, this paper employs the comple...

This paper develops an integrated framework to forecast the volatility of crude oil prices by considering the impacts of extreme events (structural breaks). The impacts of extreme events are vital to improving prediction accuracy. Aiming to demonstrate the crude oil price fluctuation and the impacts of external events, this paper employs the Comple...

Our work presents several mechanisms to calculate indicative prices for forex and cryptocurrency markets in terms of a numeraireNumeraire-free market. One of the mechanisms is tailored for the practitioner and is thus accompanied by analytic estimates that maximize its computational efficiency. Additionally, we discuss how to leverage the prices pr...

This paper aims to extend downside protection to a hedge fund investment portfolio based on shared loss fee structures that have become increasing popular in the market. In particular, we consider a second tranche and suggest the purchase of an upfront reinsurance contract for any losses on the fund beyond the threshold covered by the first tranche...

Hedge funds have recently become popular because of their low correlation with traditional investments and their ability to generate positive returns with a relatively low volatility. However, a close look at those high-performing hedge funds raises the questions on whether their performance is truly superior and whether the high management fees ar...

This paper proposes a framework to analyze hedge funds fee arrangements in which the portfolio construction is determined by the hedge fund manager and the fees are determined via an optimal equilibrium between the manager and the investor. In this setting, fees include management fees ( α ) and performance fees ( β ). We select the paradigm of Exp...

The asset management business is driven by fee structures. In the context of hedge funds, fees have usually been a hybrid combination of two different types, which has coined a well-known business term of “2 and 20”. As an attempt to provide better alignment with their investors, in a new context of low interest rates and lukewarm performance, a ne...

This article tries to enhance the current Gaussian distribution paradigm for modeling asset returns by emphasizing two points. It proposes a model which captures fat tails and skewness, and takes into account distinct market regimes. Therefore, an alpha-stable regime-switching model is proposed. The implications of this model on asset management ar...

Risk analytics has been popularized by some of the today's most successful companies through new theories such as enterprise risk management. Maximizing the benefit from investments on projects can be more based on the correlation structure dynamically from various different sources. It becomes very important to assess the forecasting performance o...

This paper investigates and compares the performances of the optimal portfolio selected by using the Orthogonal GARCH (OGARCH) Model, Markov Switching Model and the Exponentially Weighted Moving Average (EWMA) Model in a fund of hedge funds. These models are used to calibrate the returns of four HFRX indices from which the optimal portfolio is cons...

We consider portfolio management strategies where the investment style switches based on the value of a crisis indicator. A variety of strategies is considered in historical backtests on different datasets. Our findings show that certain simple switching strategies achieve statistically significant out-performance when compared to the equally-weigh...

This article investigates the use of a regime-switching model of returns for the asset allocation decision of a fund of hedge funds. In each time period, returns follow a multi-variate normal distribution from one of two possible regimes, corresponding to periods of “normal” and “distressed” markets. The prevailing regime in any given period is det...

This paper extends the structural credit model with underlying stochastic volatility to a multidimensional framework. The model combines the Black/Cox
framework with the Heston model interpreting the equity of a company as a down-and-out barrier call option on the company's assets. This implies a combination
of local and stochastic volatility on th...

In this paper we study a multivariate extension of a structural credit risk model, the CreditGrades model, under the as-sumption of stochastic volatility and correlation between the assets of the companies. The covariance of the assets fol-lows two popular models which are non-overlapping extensions of the CIR model to dimensions greater than one,...

This paper presents a new factor model for the term structure of futures prices of commodities. This model fills a gap in the literature by providing not only flexibility on the deterministic drivers of the term structure's (TS) curve but also a clear meaning of the stochastic factors implied by the model. These benefits allow the user of the model...

This paper presents a structural credit model with underlying stochastic volatility, a CIR process, combining the Black/Cox framework with the Heston Model. We allow to calibrate a Heston Model for a non-observable process as underlying of the Black/Cox Model. A closed-form solution for the price of a down-and-out call option on the assets with the...

We assume a financial market governed by a diffusion process reverting to a stochastic mean which is itself governed by an unobservable ergodic diffusion, similar to those observed in electricity and other energy markets. We develop a moment method algorithm for the estimation of the parameters of both the observable process and the unobservable st...

Risks are traditionally defined as the combination of probability and severity, but are actually characterized by additional factors. We believe the characteristics of risks include uncertainties, dynamics, dependence, clusterings and complexities, which motivate the utilization of various operational research tools. The objective of this issue is...

For risky investments, like private equity or hedge funds, default risk plays a prominent role. However, the accordant literature on portfolio optimization mostly disregards default risk and accordingly skewed return distributions. This paper presents a realistic and tractable framework for a portfolio optimization including default risk. Default i...

This paper analyzes an intensity-based approach for equity modeling. We use the Cox–Ingersoll–Ross (CIR) process to describe the intensity of the firm's default process. The intensity is purposely linked to the assets of the firm and consequently is also used to explain the equity. We examine two different approaches to link assets and intensity an...

The evolution of credit derivatives has inspired many researchers to investigate the behaviour of credit spreads. Today the
growing consensus is that the equity option market provides sufficient information to estimate latent credit parameters. Hull
et al. (J. Credit Risk 1(1):3–28, 2005) propose a clever approach to estimate credit spreads from th...

Risks are traditionally defined as the combination of probability and severity, but are actually characterized by additional factors. We believe the characteristics of risks include uncertainties, dynamics, dependence, clusterings and complexities, which motivate the utilization of various operational research tools. The objective of this issue is...

This paper assumes a structural credit model with underlying stochastic volatility combining the Black/Cox approach with the Heston model. We model the equity of a company as a barrier call option on its assets. The assets are assumed to follow a stochastic volatility process; this implies an equity model with most documented stylized facts incorpo...

In this paper we obtain closed-form expressions for the price of an European Call option on constant-proportion portfolio insurance strate-gies (CPPI). CPPIs are path-dependent derivatives themselves where the underlying typically is a market index or a fund portfolio. We de-scribe and explain the functionality of CPPIs, showing closed-form ex-pres...

In this paper we obtain closed-form expressions for the price of an European call option on constant-proportion portfolio insurance strategies (CPPI). CPPIs are path-dependent derivatives themselves where the underlying typically is a market index or a fund portfolio. We describe and explain the functionality of CPPIs, showing closed-form expressio...

Purpose
– The purpose of this paper is to deal with the different phases of volatility behavior and the dependence of the variability of the time series on its own past, models allowing for heteroscedasticity like autoregressive conditional heteroscedasticity (ARCH), generalized autoregressive conditional heteroscedasticity (GARCH), or regime‐switc...

In this paper, we propose a method to price collateralized debt obligations (CDO) within Merton's structural model on underlyings with a stochastic mean-reverting covariance dependence. There are two key elements in our development, first we reduce dimensionality and complexity using principal component analysis on the assets' covariance matrix. Se...

This paper describes the investment universe of hedge funds from a perspective which is at the same time mathematical in nature and practical in its objectives. It addresses the investment opportunities that hedge funds pur-sue, the mathematical techniques to understand their performance, the portfo-lio construction tools needed to construct invest...

This paper introduces a new theoretical framework to price hedge funds' equity. It is inspired on the famous framework of Black and Cox for the valuation of companies' equity as call options. Our structural model describing hedge funds uses barrier options (i.e. down-and-out call options as well as up-and-out put options) to allow for the special s...

In this paper we propose two first-passage-time approaches for pricing debt and equity when the firm is able to restructure its debt as an alternative to liquidation. In contrast to other first passage models that account for reorganization, our approaches allow the firm to restructure its debt by changing its maturity and/or its face value. The fi...

In this paper we develop a formula for the Liquidity Premium of constant leverage strategies (CLS). These financial products are path dependent options where the underlying typically is a hedge fund portfolio. We describe and explain the functionality of CLSs, showing a closed form expression for the price of a CLS on a hedge fund assuming a Geomet...

This paper proposes a method to price spread options on stochastically correlated underlying assets. Therefore it provides a more realistic ap-proach towards dependence structure. We generalize a constant corre-lation tree model developed by Hull (2002) and extend it by the notion of stochastic correlation. The resulting tree model is recombining a...

This paper introduces a new theoretical framework to price hedge funds' equity. It is inspired on the famous framework of Black and Scholes for the valuation of companies' equity as call options. Our structural model describing hedge funds uses barrier options (i.e. down-and-out call options as well as up-and-out put options) to allow for the speci...

In recent years, credit risk evaluation and credit default prediction have attracted a great deal of interests from both practitioners and regulators in the financial industry. This paper reviews various methods in credit risk evaluation. We demonstrate the use of a scorecard in a bank and validate the performance of such a scorecard through analys...

In this paper we consider a portfolio optimization problem where the underlying asset returns are distributed as a mixture of two multivariate Gaussians; these two Gaussians may be associated with “distressed” and “tranquil” market regimes. In this context, the Sharpe ratio needs to be replaced by other non-linear objective functions which, in the...

In this paper we add a Black and Cox (1976) approach for debt and equity valuation to the common practice of reorganization leading to a more realistic setting. We introduce first passage models in order to allow for both reorganization as well as liquidation before maturity time. This paper considers two types of settings. The first one is a first...

In this paper we present a historical account of the evolution of mathematics and risk management over the last 20 years. In it, we will focus primarily on present credit market developments and we give an account of some new credit derivatives: collateralised fund obligations. structures, combining stochastic processes and statistics to numerous a...

In this paper we present a historical account of the evolution of mathematics and risk management over the last twenty years. In it, we will focus primarily on present credit market developments and we give an account of some new credit derivatives: collateralized fund obligations.

Canadian winters are extreme: cold and snow are a fact of everyday life. Canada spends over $1Bn every year removing snow. As one example, consider the city of Montreal. The city spends over $50M every year removing snow, about 3% of its total budget. It does that through a fixed-price contract agreement with a third party, which starts on November...

Partial dierential equations proved to be a fundamental tool as the derivatives market de- veloped in the seventies. As markets continue into more sophisticated territory, such as credit trading, dierential equations continue to play an important role, with the added quali…er that the equations that arise are now much more complex. This paper prese...

In this paper we obtain an estimate for the Thomas-Fermi density which plays a role in the analysis of the atomic enegry asymptotics. Such estimate has obvious number-theoretic features related to the radial symmetry of a certain Schrodinger operator, and we use number-theoretic methods in our proof. From the technical viewpoint, we also simplify a...

Collateralized Debt Obligations (CDO) are structured credit vehicles that redistribute credit risk to meet investor demands for a wide range of rated securities with scheduled interest and principal payments. CDOs are securitized by diversified pools of debt instruments. Recent developments in credit structuring technology include the introduction...

A new method is developed for estimating the spectral measure of a multivariate stable probability measure, by representing the measure as a sum of spherical harmonics.

This is a quantitative form of the non--periodicity of almost all zero--energy orbits for the Hamiltonian H = jj + VTF (jxj) on R = f(x; ) j x 2 R ; 2 g. In fact, an easy computation shows that a zero--energy orbit with angular momentumOmega is periodic if and only if the derivative F is a rational multiple of (see [1].) Hence, Theorem 0.1 shows th...

Value at risk (VaR) is an industrial standard for monitoring financial risk in an investment portfolio. It measures potential losses within a given confidence interval. The implementation, calculation, and interpretation of VaR contains a wealth of mathematical issues that are not fully understood. In this paper we present a methodology for an appr...

Recent statistical analysis of a number of financial databases is summarized. Increasing agreement is found that logarithmic equity returns show a certain type of asymptotic behavior of the largest events, namely that the probability density functions have power law tails with an exponent alpha~3.0. This behavior does not vary much over different s...

There are two natural commuting self-adjoint operators in the enveloping algebra of the Heisenberg group: the Heisenberg sublaplacianΔHand the central elementT=−i∂/∂t. The joint spectral theory of these operators is investigated by means of the Laguerre calculus. Explicit convolution kernels are obtained for a large class of functionsΦ(−ΔH, T). In...

this paper we will simply refer to them as "antisymmetric" wave functions. For each Z, call N(Z) the smallest number for which E(Z) = E(Z; N ). It is an interesting problem to obtain sharp estimates for N(Z). The sharpest known result appears in [8], where the reader will find a discussion of the history of the problem. In particular, N(Z)=Z ! 1 as...

. For an atom of nuclear charge Z, the ground state energy is defined to be the lowest possible value of the energy Hamiltonian. We describe an algorithm to produce rigorous lower bounds for the ground state energy of atoms as well as its implementation. 0. Introduction. The Hamiltonian for an atom of charge Z is H = Z X i=1 Theta (Gamma 1 2 Delta...

This article contains a combination of rigorous mathematical results with others of a more speculative nature and more physical content. The bibliography, necessarily incomplete, contains numerous missing pieces that this brief overview lacks. Mean--Field Theory. The analysis of (3) begins with the development of a simplified picture of HZ;N throug...

Consider an atom consisting of N quantized electrons at positions x
i and a nucleus fixed at the origin. The Schrödinger Hamiltonian of such a system is given by $${H_{Z,N}} = \sum\limits_{i = 1}^N {\left( { - {\Delta _{{x_i}}} - \frac{Z} {{\left| {{x_i}} \right|}}} \right)} + \frac{1} {2}\sum\limits_{i \ne j} {\frac{1} {{\left| {{x_i} - {x_i}} \ri...

this article. Semiclassical asymptotics. The most immediate consequence of mean field theory is that the original hamiltonian

this paper lies in the asymptotic formula, as Z goes to infinity, for the atomic energy

We present a simple argument which gives a bound on the ionization energy of large atoms and at the same time proves the bound on the excess charge of Fefferman and Seco[1]. 1 Introduction An atom of nuclear charge Z with N electrons is described by the Schrodinger operator HN;Z = N X i (GammaDelta i Gamma Z jx i j ) + X 1i!jN 1 jx i Gamma x j j (1...

In [FS1] we announced a precise asymptotic formula for the ground-state energy of a non-relativistic atom. The purpose of this paper is to establish an elementary inequality that plays a crucial role in our proof of that formula. The inequality concerns the Thomas-Fermi potential VTF = -y(ar) / r, a > 0, where y(r) is defined as the solution of ì y...

this paper is to give a brief joint expository presentation of the proof of Theorem 1. We refer the reader to (7, 8, 9, 10, 11, 12, 13 and 16) for accurate statements and detailed proofs of what follows. Before we preceed to the proof, we recall a few basic facts about Thomas-- Fermi theory. We refer the reader to (17) for a comprehensive review. W...

Value at Risk is a measure of risk exposure of a portfolio and is defined as the maximum possible loss in a certain time frame, typically 1-20 days, and within a certain confidence, typically 95%. Full valuation of a portfolio under a large number of scenarios is a lengthy process. To speed it up, one can make use of the total delta vector and the...

The ground state energy of an atom is defined to be lowest possible value of the energy Hamiltonian. This work describes an algorithm to obtain lower bounds for the ground state energy of atoms, together with its implementation. The results are within a few precent of the upper bounds given by Hartree--Fock's method. 1 Acknowledgements: It is a gre...

This paper is part of a series [FS2: : : 7] proving the asymptotic formula announced in [FS1] for the ground-state energy of an atom. Our goal here is to give precise estimates for the sum of the negative eigenvalues of an ordinary differential operator (1) H = Gamma

this paper, we apply the results of IFS2] to study the density (1) p(x): I)12. Ek _0 We will introduce a simple approximation ps(x), and estimate p- psi. Our goal is to prove the asymptotic formula announced in IFS1] for the ground state energy of an atom. This requires estimates for p - p, in weighted Sobolev norms of order -1, which we will deriv...

this paper is to estimate ae Gamma ae sc for a particular potential V TF on

. We extend Van der Corput's method for exponential sums to study an oscillatory term appearing in the quantum theory of large atoms. We obtain an interpretation in terms of classical dynamics and we produce sharp asymptotic upper and lower bounds for the oscillations. A non--relativistic atom of nuclear charge Z fixed at the origin, and N quantize...

this paper is to describe the analysis involved in understanding the sum Psi Q (Z) as a function of Z, which turns out to be an adaptation of a well--known method in analytic number theory developed mostly by Van der Corput to understand the number of lattice points in a large circle. We begin with a few remarks about analytic number theory. Number...

We extend Van der Corput's method for exponential sums to study an oscillating term appearing in the quantum theory of large atoms. We obtain an interpretation in terms of classical dynamics and we produce sharp asymptotic upper and lower bounds for the oscillations.

In this paper we address a question posed by M. and T. Hoffmann-Ostenhof, which concerns the total spin of the ground state of an atom or molecule. Each electron is given a value for spin, ±1/2. The total spin is the sum of the individual spins.

Value at Risk is a measure of risk exposure of a portfolio and is defined as the maximum possible loss in a certain time frame, typically 1-20 days, and within a certain confidence, typically 95%. Full valuation of a portfolio under a large number of scenarios is a lengthy process. To speed it up, one can make use of the total delta vector and the...

> (x); y(0) = 1; y(1) = 0: (0:1) Define F(OmegaGamma = Z ` y(x) x GammaOmega 2 x 2 ' 1 = 2 + dx; Omega 2 (0 ;Omega c ); where a+ = max(a; 0), and a numberOmega c will be defined at the beginning of Section 2. The function F(OmegaGamma depends smoothly onOmega [41], and the main result in [21] is as follows: 1 2 Chapter 1 Theorem 0.1. F 00(OmegaGamm...

Quantum mechanics is an area which, over the last ten years or so, has sparked a respectable amount of rigorous computer assisted work (see, for example [9, 13, 20, 39, 38], and their applications in [10, 11, 12, 3, 4, 5,14,15,16,17,18,19, 20]). The purpose of this review is to select a piece of that body of work, and to give a more or less detaile...

We extend Van der Corput's method for exponential sums to study an oscillatory term appearing in the quantum theory of large atoms. We obtain an interpretation in terms of classical dynamics and we produce sharp asymptotic upper and lower bounds for the oscillations.

In the present paper we consider Neumann Laplacians on singular domains of the type “rooms and passages” or “combs” and we show that, in typical situations, the essential spectrum can be determined from the geometric data. Moreover, given an arbitrary closed subset S of the non-negative reals, we construct domains Ω = Ω(S) such that the essential s...