2007 Stanford-Tsukuba-WCQF Joint Workshop

2007 Stanford-Tsukuba-WCQF Joint Workshop

Speaker: Howard Bomze

Title: TBA

Speaker: Alexander Cherny

Title: Coherent Acceptability Indices

Abstract:

A basic characteristic of a trade is its degree of quality, or the degree of acceptability. Known measures of acceptability/quality are Sharpe Ratio, RAROC, and Gain-Loss Ratio. In a recent paper with D. Madan we addressed the question: Which axioms a proper measure of acceptability should satisfy? We formulated a set of axioms defining a coherent acceptability index and provided a characterization theorem for this class. The characterization theorem shows that a coherent acceptability index is closely related to a family of coherent risk measures with increasing degree of risk aversion. The notion of a coherent risk measure was introduced by Artzner, Delbaen, Eber, and Heath.

In the talk I will describe the axioms and the representation theorem and then discuss which of the classical performance measures satisfy these axioms. After that, I will compare between different coherent acceptability indices and introduce some new ones, having the most desirable properties. The basic tool for comparing between different indices will be the notion of a coherent state-price density. It is worth noting that coherent indices provide new approaches to measuring the degree of market efficiency, pricing and hedging, as well as portfolio choice.

Speaker: Darrell Duffie

Title: TBA

Speaker: Jean-Pierre Fouque

Title: Default probabilities, credit derivatives, and computational issues

Abstract:

We show that perturbation methods are useful in approximating default probabilities in the context of first passage stochastic volatility models. We then consider the case of many names and we discuss various ways of creating correlation of defaults. In highly-dimensional models, Monte Carlo simulations remain a powerful tool for computing prices of credit derivatives such as CDO's tranches and associated greeks. We propose an interacting particle system approach for computing the small probabilities involved in these financial instruments.

Speaker: Lisa Goldberg

Title: TBA

Speaker: Xin Guo

Title: Connecting singular and switching controls, with applications to (ir)reversible investment

Abstract:

Abstract: Analysis of (ir)reversible problems from mathematical economics has evolved considerably from the initial heuristics to the more sophisticated and standard stochastic control approach. In this talk, we discuss a new theoretical connection between singular controls of finite variation and a class of switching controls. This correspondence provides a novel methodology for solving explicitly high-dimensional singular control problems, and enables us to extend the theory of (ir)reversible investment. In particular, both sufficient and necessary conditions for the well-known smooth fit principle along with the regularity of the value functions are given. And when the payoff functions satisfy the usual Inada conditions, the boundaries between action and no-action regions are smooth and strictly monotonic as postulated and exploited in the existing literature. Consequently, our result links singular controls and Dynkin games through sequential optimal stopping problems.

This talk is based on joint work with P. Tomecek of Cornell.

Speaker: Takaki Hayashi

Title: Nonsynchronous covariation with application to high-frequency finance

Abstract:

There has been growing importance of the use of high-frequency data in financial risk management for the last decade. Among notorious features of such data is nonsynchronicity, i.e., market prices are recorded at irregular times in a nonsynchronous manner, a reflection of the reality of actual trading. This feature can be problematic when methods developed for synchronous data are applied. In this study, we tackle a statistical estimation problem of the covariance for high-frequency data. We formulate the problem in a framework with semimartingales sampled at nonsynchronous stopping times. The results extend the existing studies on realized volatility type estimators that are based on synchronous samples. (Joint work with Professor Nakahiro Yoshida.)
Key words: discrete sampling; high-frequency data; martingale central limit theorem; nonsynchronicity; quadratic variation; realized volatility; stopping time; semimartingale

Speaker: Masaaki Kijima

Title: A Latent Process Model for the Pricing of Corporate Securities (Joint work with Teruyoshi Suzuki and Keiichi Tanaka)

Abstract:

We propose a structural model with a joint process of tangible assets (marker) and firm status for the pricing of corporate securities. The firm status process is assumed to be latent or unobservable, and default occurs when the firm status reaches a default threshold. The marker process is observable and assumed to be correlated with the latent firm status. The recovery upon default is a fraction of tangible assets at the time of default. When the two processes are perfectly correlated, our model is reduced to the seminal Black-Cox model. Numerical examples reveal that our model is consistent with empirical findings observed in the corporate bond market.

Speaker: Toshio Kimura

Title: Household Optimal Portfolios: The Role of Debt Repayment Term Decision

Abstract:

Building on the Merton's (1971) consumption-portfolio problems with income, we obtain explicit link between debt-repayment term and consumption-investment policy for households who holds long-term mortgage debt. Depending on interest rate process, optimal accelerated debt-repayment dampens household's financial wealth accumulation, which results in larger risky investment share to total financial wealth. Using micro data of Japanese households, we find that accelerated debt-repayment has positive effect on the risky asset share conditional on asset holding, whereas such dampened financial wealth deters owning risky asset. These findings provide qualitative explanation for the hump-shaped age-related pattern in risky asset investment, particularly observed among households with mortgage debt.

Speaker: David Luenberger

Title: TBA

Speaker: Naoki Makimoto

Title: Optimal time to invest under uncertainty with a scale change

Abstract:

In this talk, we investigate the optimal investment problem to maximise expected discounted payoff of a project whose value is given by a product of two processes: a geometric Brownian motion representing continuous fluctuation over time and a birth-death process which gives a discontinuous scale change. It turns out that the optimal policy is of threshold type whose thresholds depend on the current state of the birth-death process. For 2-state case, the problem can be solved explicitly by using Bellman equations and smooth pasting conditions. On the other hand, the problem becomes much involved when there are multiple states. We exploit the structure of the optimal policy and the form of the value functions which provide a means to solve the problem numerically.

Speaker: Hidetaka Nakaoka

Title: Option Valuation of Oil & Gas E&P Projects by Futures Term Structure Approach

Abstract:

Oil & gas E&P projects have been one of the typical subjects for real options approach. However, there are still some significant difficulties for business practitioners to apply real options to actual E&P projects due to the tracking problems in incomplete markets, while misinterpretation of the recoverable volume of the reserves under uncertainty have caused serious accounting problems to super major oil companies these days. This presentation is intended to treat these problems and to provide a more realistic real options approach to the management of investors. I will firstly present the effect of the reserve risks, by introducing the uncertainty into the recoverable volume of the oil and gas reserves in the producing fields. The empirical results clearly indicate that it can give significant impacts on the valuation of the rights to explore and exploit the oil and gas fields. Secondly, I will introduce a new approach, which can provide an effective solution to the tracking problems of the underlying asset value and its volatility, by verifying that the underlying asset price can be valued by application of the term structure of futures prices to the net cash flow of the projects. This approach can be widely applied not only to the valuation of oil & gas E&P business, but also to those of long term investments under uncertainty in the other business fields, where futures markets are available for their commodities.

Speaker: Katsumasa Nishide

Title: Regime Uncertainty and Investment Policy (joint work with Ernesto Kazuhiro Nomi)

Abstract:

We construct a real options model in which there may be a regime change at a pre-specified future time, and study the effect of regime uncertainty on the firm's strategic investment decision, taking into consideration the time of the regime change and the probability of each regime state. We show that firms will require a higher trigger value as the time of the change approaches, and that the trigger value at the time is determined by the regime structure, and independent of its probability. Our model effectively explains why South American countries have fewer investments just before an presidential election that may cause a big policy change.

Key words: Real options, Policy change, regime uncertainty.

Speaker: Naoto Oshiro

Title: Quantification of Sovereign Risk: Using the Quasi-Balance Sheets

Abstract:

Sovereign risk evaluation has various different aspects from those of corporate. One of major difficulties is lack of disclosed data for their macroeconomics performances. Furthermore, most of these disclosed data are for part of flow related such as GDP, current account, interest payment etc., but not for stock data comprising sovereign’s macroeconomic balance sheets. Thus, sovereign risk evaluation, to some extent, depends on the qualitative investigations. For example, sovereign credit rating by rating agencies are based on qualitative researched by rating analyst as well as quantitative analysis of macroeconomic data and country risk ranking published by Institutional Investor and Euromoney is based on summary of questionnaire from a hundred of professional’s views. Nevertheless, according to our experiences from corporate credit risk, the balance sheet information is quite helpful for better evaluation and the option pricing approach is quite commonly accepted by the professional. To improve sovereign risk evaluation performance, we propose a new quantitative approach to use the information from sovereign’s quasi-balance sheets. We demonstrate this approach can be applicable to larger numbers of countries rather than using market price information such as sovereign bond prices or CDS.

Speaker: George Papanicolaou

Title: TBA

Speaker: Jim Primbs

Title: Receding Horizon Control for Constrained Portfolio Optimization

Abstract:

Receding horizon control is a methodology that relies on repeated, on-line optimizations to control a system. It has been used successfully to control many systems with constraints. We develop receding horizon control for stochastic systems with constraints. We are able to solve on-line optimizations as semi-definite programs, indicating that relatively large problems can be tackled. We demonstrate the methodology on a constrained index tracking problem.

Speaker: Knut Solna

Title:Multiname and Multiscale Default Modeling

Abstract:

We analyze the role of stochastic volatility in the case of the credit derivatives market. We consider a simple reduced form modeling approach for multiname defaults. The model is based on the Vasicek or Ornstein-Uhlenbeck model for the hazard rates of the underlying names. We analyze the impact of volatility time scales on the default distribution and CDO prices and demonstrate how correlated fluctuations in the parameters of the name hazard rates affect the loss distribution.

Speaker: Yuji Yamada

Title: Optimal Design of Wind Derivatives

Abstract:

In this work, we develop a methodology to synthesize wind derivatives for optimally hedging certain risk in wind power energy businesses. We generalize the standard mean variance hedge based on a nonparametric regression technique, and estimate the hedge effect of wind derivatives using empirical data. A simultaneous optimization of loss and payoff functions for wind derivatives is also demonstrated.

Speaker: Makoto Yamazaki

Title: An Examination of The Book-to-Market Effect In The Japanese Stock Market: Risk or Mispricing?

Abstract:

There are so-called “ value effects” in the stock market. In other words, the stocks with high earnings-price ratio, high book-to-market ratio, and high cashflow-price ratio tend to yield higher returns than the market return. However, we have not agreed as to why these stocks yield higher returns: reward for the risk or mispricing? In this work, we bring up the “High-Book-to-Market effect (High-BTM effect)” and examine whether high returns on High-BTM stocks are caused by either “risk” or “mispricing”, using the skewness of the stock returns.

We form three different hypotheses in terms of the skewness of the stock returns based on these “risk” and “misprining” theories. The first is that the market requests a risk premium against the coskewness risk. The second is that a stock return with high distress risk has negative skewness. The last is that a stock return with mispricing (a return on the undervalued stock) has positive skewness. In testing these hypotheses, we apply the asset pricng model including coskewness and the prediction model for skewness to the data of the Japanese equity market from 1980 to 2005, following the Fama and MacMeth procedure employing the time-series t tests of estimated risk premiums . We find that (1) the estimated risk premium for coskewness is not statistically significantly different from zero and (2) high BTM stocks tend to have positive skewness in the skewness prediction model. We interpret the overall results in favor of the mispricing hypothesis.

Speaker: Thaleia Zariphopolou

Title:Optimal asset allocation under forward performance criteria

Speaker: Jianfeng Zhang

Title: Optimal contracting with random time of payment and outside options

Abstract:

We consider continuous-time Principal-Agent problems in which the payoff is delivered at an optimal random time. Results are given in cases of moral hazard and/or adverse selection. The optimal time of payment depends on the agent's and the principal's outside options. In examples with CARA utilities, under specific "stationarity" conditions on the outside options, it is not optimal for the principal to give the agent the option to exercise the contract at a random time. However, in general, the optimal payment time is typically random.

The methodology we use for the general theory is the stochastic maximum principle and its link to Forward-Backward Stochastic Differential Equations and their reflected version, appropriate for optimal stopping problems. This is a joint work with Jaksa Cvitanic and Xuhu Wan.

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