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Seminar: Autumn 2005

Stanford Financial Mathematics Seminar Schedule

Date Speaker Affiliation Talk Title
(click to see Abstract)


Peter Hansen Economics, Stanford Realized Variance and Market Microstructure Noise  
10/14 Peter Bossaerts

Prof. of Econ. & Managem. and Prof. of Finance,

California Institute of Technology

The Paradox Of Asset Pricing slides pdf
10/21 Valdo Durrleman Mathematics, Stanford Coupling smiles in FX markets
10/28 no seminar this week      


12:00 Noon

Sequoia Room 200

Juyoung Lim UT Austin A numerical algorithm for indifference pricing in incomplete markets Note early start time
Jeremy Evnine Evnine-Vaughan Associates, Inc.    
11/11 Peter Knez CIO, Global Head of Fixed Income, Barclays Global Investors, San Francisco
11/18 Ronnie Sircar Operations Research & Financial Engineering, Princeton University Games with Exhaustible Resources
11/25 no seminar this week      
12/2 Sanjiv Das Santa Clara University, Leavey School of Business Information Structure and Investor Sentiment Extraction using
the Internet

slides pdf

Realized Variance and Market Microstructure Noise

Peter Hansen (Economics, Stanford)

We study market microstructure noise in high-frequency data and analyze its implications for the realized variance (RV) under a general specification for the noise. We show that kernel-based estimators can unearth important characteristics of market microstructure noise and that a simple kernel-based estimator dominates the RV for the estimation of integrated variance (IV). An empirical analysis of the Dow Jones Industrial Average stocks reveals that market microstructure noise is time-dependent and correlated with increments in the efficient price. This has important implications for volatility estimation based on high-frequency data. Finally, we apply cointegration techniques to decompose transaction prices and bid-ask quotes into an estimate of the efficient price and noise. This framework enables us to study the dynamic effects on transaction prices and quotes caused by changes in the efficient price.

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The Paradox Of Asset Pricing

Peter Bossaerts (California Institute of Technology)

The book argues that theory is not necessarily to blame for the poor scientific record of asset pricing, but empirical methodology. There are at least two problems: (i) empirical methodology relies too much on the untenable assumptions of correct ex ante beliefs and stationarity, which are not part of the theory; (ii) it is focused on using historical data from the field, overlooking the value of experimentation with financial markets. It is not easy to address these two problems, but the book demonstrates that it can be done, without losing much of the rigor we have come accustomed to. What is perhaps most exciting is that the record of modern asset pricing theory looks very different as a result.
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Coupling smiles in FX markets

Valdo Durrleman (Mathematics, Stanford)

Consider the world three major currencies, EUR, JPY, and USD, and their three corresponding exchange rates. An elementary arbitrage argument gives any of the three exchange rates as a function of the other two. In this talk, we are interested in a similar problem for options on these currencies. More precisely, we would like to reconstruct the implied volatility smile of one currency given the other two.

The talk is based on an idea of Nicole El Karoui and on discussions with Andres Villaquiran.

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A numerical algorithm for indifference pricing in incomplete markets

Juyoung Lim (UT Austin)

This paper proposes a numerical algorithm to compute the indifference price and risk monitoring strategy of a contingent claim in incomplete markets with the exponential preference. Using the duality between the exponential optimal investment problem and the minimal relative entropy problem, we recast the option writer’s optimal investment problem as a minimax problem and derive the complete procedure of finding the solution numerically. The Lagrange multiplier process emerges from the iterative minimax optimization procedure, and is shown to be connected to the “delta” of the indifference price. We present the numerical results of the algorithm with two representative examples, one with the nontradable assets and the other with the stochastic volatility model. The results show that the algorithm computes not only the indifference price but also the indifference “delta” very efficiently.
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Jeremy Evnine (Evnine-Vaughan Associates, Inc.)

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Games with Exhaustible Resources

Ronnie Sircar (Princeton University)
We study the effect of limited resources in a non-zero sum differential Cournot game between two oil producers. Solutions are characterized by a system of fully nonlinear PDEs which are analyzed by asymptotic methods in the inexhaustible limit, and by vanishing viscosity numerical solutions.

Joint work with Chris Harris and Sam Howison.

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Information Structure and Investor Sentiment Extraction using the Internet

Sanjiv Das (Santa Clara University, Leavey School of Business)

This talk will present on-going research for using the web for financial analysis in two domains: information content and the sociological structure of investor interaction.

Extracting sentiment from text is a hard semantic problem. We develop a methodology for extracting small investor sentiment from stock message boards. The algorithm comprises different classifier algorithms coupled together by a voting scheme. Time series and cross-sectional aggregation of message information improves the quality of the resultant sentiment index, in the presence of slang and ambiguity. Empirical applications evidence a relationship with stock
returns -- visually, using phase-lag analysis, pattern recognition and statistical methods. Sentiment has an idiosyncratic component, and aggregation of sentiment across stocks tracks index returns more strongly than with individual stocks. The evidence suggests that market activity influences small investor sentiment in short time frames. The algorithms developed in this paper may be used to assess the impact on investor opinion of management announcements, press releases, third-party news, and regulatory changes.

We will also explore the sociological mechanics underlying the impounding of information into prices, and consequent implications for portfolio construction. Graph-theoretic techniques applied to the web network of stock discussion allow portfolio managers to classify stocks into two types, communities of connected stocks, and singletons, with the former outperforming the latter in a risk-adjusted
sense. The sociological concept of centrality implemented via eigenvector decompositions of the web graph finds that stocks with high centrality co-vary relatively more with other stocks, suggesting greater analyst focus. Thus classifying stocks into financial communities provides a novel way of looking at risk-return trade-offs, focusing analyst attention, and offers new diversification insights to portfolio managers.

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