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Diversified Statistical Arbitrage: Dynamically Combining Mean Reversion and Momentum Strategies by James Velissaris Abstract: This paper presents a quantitative investment strategy that is capable of producing strong risk-adjusted returns in both up and down markets. The strategy combines mean reversion and momentum investment strategies to construct a diversified statistical arbitrage approach. The mean reversion strategy decomposes stock returns into market and idiosyncratic return components using principal component analysis. The momentum strategy uses technical trading rules to trade momentum at the industry sector level. Dynamic portfolio optimization is utilized to rebalance exposures as the market environment evolves. The combined strategy was able to generate strong risk-adjusted returns in 2008 as the market declined, and in 2009 as the market rallied. The strategy has proven to be robust across two very different market environments in 2008 and 2009.
Keywords: Arbitrage, Principal Component Analysis, Statistical Arbitrage, Quantitative Finance Discuss this paper
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by Binh Doa and Robert Faff Abstract: We re-examine and enhance evidence on ‘pairs trading’ most prominently documented in US markets by Gatev, Goeztmann and Rouwenhorst (1999, 2006). Extending their original analysis to June 2008, we confirm a continuation of the declining trend in profitability. However, contrary to popular belief, we find that the rise in hedge fund activity is not a plausible explanation for the decline. Instead, we observe that the underlying convergence properties are less reliable - there is an increased probability that a pair of close substitutes over the past 12 months are no longer close substitutes in the subsequent half year. This fragility in the Law of One Price dynamics reflects increased fundamental risks, or uncertainty in market perception of relative values of the paired securities. Nevertheless, we still find more than half the selected pairs are either profitable or very profitable. Moreover, we demonstrate some success in identifying these successful cases by augmenting the original pair matching method to incorporate the time series aspect of historical prices, and/or by focusing on industries with a high level of homogeneity. Discuss this paper
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a book kindly made freely available by Phelim Boyle & Feidhlim Boyle
Preface xi 1 Introduction 1 2 Markets and Products 15 3 Why there are No Free Lunches 37 4 Pricing by Replication 49 5 The Quest for the Option Formula 71 6 How Firms Hedge 95 7 How Investors use Derivatives 115 8 Disasters: Divine Results Racked by Human Recklessness 135 9 Credit Risk 155 10 Financial Engineering: Some Tools of the Trade 177 Discuss this paper
Preliminary version, comments are welcome. This paper finds the eigenvalues and eigenvectors of the covariance matrix associated with multi-dimensional Brownian motion and the OrnsteinUhlenbeck processes. The result is given in closed form for the onedimensional Brownian motion. In the general case it involves some numerical computations, but the overall work is a small fraction of the work required by standard methods to compute eigenvalues and eigenvectors of a covariance matrix. The results have applications in a new QuasiMonte Carlo method [1] for computing the expected value of a function depending on a Brownian Motion. 1 One-Dimensional Brownian Motion Let fW (t); t 0g be a standard Brownian motion. Consider the time points t i = T i n; 1 i n. The covariance matrix CW = (c i;j) associated with (W (t 1); : : : ; W (t n)), has the elements c i;j = min(i; j) n T: (1) Discuss this paper
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by Rama CONT and Jose da FONSECA Abstract The prices of index options at a given date are usually represented via the corresponding implied volatility surface, presenting skew/smile features and term structure which several models have attempted to re-produce. However the implied volatility surface also changes dynamically over time in a way that is not taken into account by current modeling approaches, giving rise to 'Vega' risk in option portfolios. Using time series of option prices on the SP500 and FTSE indices, we study the deforma tion of this surface and show that it may be represented as a randomly surface driven by a small number of orthogonal random factors. We identify and interpret the shape of each of these factors, study their dynamics and their correlation with the underlying index. Our approach is based on a Karhunen-Loeve decomposition of the daily variations of implied volatilities obtained from market data. A simple factor model compatible with the empirical observations is proposed. We illustrate how this approach model and improves the the well-known sticky moneyness Discuss this paper
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by J.N. Dewynne and W.T. Shaw In this article we present a simplified means of pricing Asian options using partial differential equations. We first provide a concise derivation of the well-known similarity reduction and exact Laplace transform solution. We then analyse the problem afresh as a power series in the volatility-scaled contract duration, with a view to obtaining an asymptotic solution for the low-volatility limit, a limit which presents difficulties in the context of the general Laplace transform solution. The problem is approached anew from the point of view of asymptotic expansions and the results are compared with direct, high precision, inversion of the Laplace transform and with numerical results obtained by V. Linetsky and J. Vecer. Our asymptotic formulae are little more complicated than the standard Black-Scholes formulae and, working to third order in the volatility-scaled expiry, are accurate to at least four significant figures for standard test problems. In the case of zero risk-neutral drift we have the solution to fifth order and, for practical purposes, the results are effectively exact
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by Jun Liu and Jun Pan This paper studies the optimal investment strategy of an investor who can access not only the bond and the stock markets, but also the derivatives market. We consider the investment situation where, in addition to the usual di usive price shocks, the stock market experiences sudden price jumps and stochastic volatility. The dynamic portfolio problem involving derivatives is solved in closed-form. Our results show that derivatives are important in providing access to the risk and return tradeo s associ- ated with the volatility and jump risks. Moreover, as a vehicle to the volatility risk, derivatives are used by non-myopic investors to exploit the time-varying opportunity set; and as a vehicle to the jump risk, derivatives are used by investors to dis-entangle their simultaneous exposure to the di usive and jump risks in the stock market. In addition, derivatives investing also a ects investors' stock position because of the in- teraction between the two markets. Finally, calibrating our model to the S&P 500 index and options markets, we nd sizable portfolio improvement for taking advantage of derivatives
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Dealing with Derivatives:Studies on the role, informational content and pricing of financial derivatives Prof.dr. C.G. Koedijk Part I: Microstructure studies in derivatives markets Chapter 2: Introduction to the first part 11 Chapter 3: Stock market quality in the presence of a traded option 15 3.1 Experimental design and procedures 18 3.2 Results 24 3.3 Discussion 44 3.4 Conclusion 45 Chapter 4: Insider strategies with options 47 4.1 The model 48 4.2 Market quality criteria 53 4.3 Results 56 4.4 Conclusion 70 Chapter 5: Conclusion of the first part 73 Part II: Empirical studies in derivatives markets Chapter 6: Introduction to the second part 79 Chapter 7: The skewed-t implied distribution model 83 7.1 Methodology 86 7.2 Empirical results 91 7.3 Concluding remarks 102 Chapter 8: Implied GARCH volatility forecasting 105 8.1 Methodology 108 8.2 Data 114 8.3 Empirical results 119 8.4 Concluding remarks 128 Chapter 9: Pricing the spikes in power options 131 9.1 The two regimes model for spot electricity prices 134 9.2 Model estimation results 140 9.3 Option valuation 148 9.4 Concluding remarks 161 Chapter 10: Conclusion of the second part 165 Chapter 11: Summary and concluding remarks 169 11.1 Summary first part 169 11.2 Summary second part 170 11.3 Concluding remarks and future research 172 References 175 Samenvatting (Summary in Dutch) 189 Curriculum vitae 195 Discuss this paper
This paper presents a brief introduction to the use of duality theory and simulation in financial engineering. It focuses on American option pricing and portfolio optimization problems when the underlying state space is high-dimensional. In general, it is not possible to solve these problems exactly due to the so-called Discuss this paper
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Aldo Tagliani Abstract The paper is devoted to pricing options characterized by discontinuities in the terminal condition. Finite difference schemes are examined to highlight how discontinuities can generate numerical drawbacks, as spurious oscillations. The proposed schemes are free of spurious oscillations and satisfy both the positivity requirement and maximum principle, as demanded for the financial and diffusive solution to the original Black-Scholes partial differential equation. Key words: Black-Scholes equation, Finite difference schemes, Jacobi matrix, M-matrix, nonsmooth initial conditions, positivity-preserving.1 Discuss this paper
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CLAUDIO ALBANESE AND OLIVER X. CHEN Abstract. The model introduced in this article is designed to provide a consistent representation for both the real-world and pricing measures for the credit process. We find that good agreement with historical and market data can be achieved across all credit ratings simultaneously. The model is characterized by an underlying stochastic process that takes on values on a discrete lattice and represents credit quality. Rating transitions are associated to barrier crossings and default events are associated with an absorbing state. The stochastic process has state dependent volatility and jumps which are estimated by using empirical migration and default rates. A risk-neutralizing drift is estimated to consistently match the average spread curves corresponding to all the various ratings.
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CLAUDIO ALBANESE AND ALEXEY KUZNETSOV ABSTRACT. We introduce a Poisson approximation scheme for jump processes and use it to construct numericaldiscretizations for the corresponding partial integro-differential equations. Transition probabilities are computed analytically as expansions in orthogonal polynomials to ensure that results don Discuss this paper
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Damiano Brigoƒ Cristina Capitani Fabio Mercurio Abstract In this paper we consider several parametric assumptions for the instantaneous covariance structure of the Libor market model. We examine the impact of each different parameteriza- tion on the evolution of the term structure of volatilities in time, on terminal correlations and on the joint calibration to the caps and swaptions markets. We present a number of cases of calibration in the Euro market. In particular, we consider calibration via a parameterization establishing a controllable one to one correspondence between instantaneous covariance pa- rameters and swaptions volatilities, and assess the benefits of smoothing the input swaption matrix before calibrating.
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Aurelien Alfonsi Structure of the talk Introduction et motivations The different discretization schemes The strong convergence of the schemes Weak convergence and Romberg extrapolation Conclusion: A comparative statement of the schemes Discuss this paper
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CLAUDIO ALBANESE AND OLIVER X. CHEN Abstract. The model introduced in this article is designed to provide a consistent representation for both the real-world and pricing measures for the credit process. We find that good agreement with historical and market data can be achieved across all credit ratings simultaneously. The model is characterized by an underlying stochastic process that takes on values on a discrete lattice and represents credit quality. Rating transitions are associated to barrier crossings and default events are associated with an absorbing state. The stochastic process has state dependent volatility and jumps which are estimated by using empirical migration and default rates. A risk-neutralizing drift is estimated to consistently match the average spread curves corresponding to all the various ratings. Discuss this paper
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