Titles and Abstracts
Why Distinguishing Jumps from Volatility is Difficult
This paper examines the estimation of parameters of a discretely sampled Markov process whose continuous-time sample paths are generated by a continuous Brownian term and a stochastic jump term, a realistic setting for many financial asset prices. In discretely sampled data, every change in the value of the variable is by nature a discrete jump, yet we wish to estimate jointly from these data the underlying continuous-time parameters driving the Brownian and jump terms. The paper focuses on the effect of the presence of jumps on the estimation of the volatility parameters, and the effect of the presence of the continuous Brownian part on the estimation of the jumps parameters, in the context of maximum-likelihood and method of moments estimators. These effects are studied as a function of the frequency at which the continuous-time process is sampled.
Optimal security design and diversification in financial markets with non-tradeable risks
Nicole El Karoui, Pauline Barrieu
We focus on the optimal characterization of a security based on a non-tradeable risk. On one hand, a bank is exposed to this particular risk and is willing to partly transfer this risk via a structured product. On the other hand, an investor is motivated by the diversification potential of such a security. Both agents have the opportunity to invest on the financial market through an optimal strategy that includes their respective global position. The bank's objective is then to determine the structure of the contract, maximizing its expected utility, where the price is given by the investor.
Based on an exponential utility criterion, the main result is that the optimal security is always proportional to the bank's exposure, and most importantly, is independent of any assumption on uncertainty, while the price is given by an indifference pricing rule.
The Future of Energy Markets
The energy markets in the developed countries underwent a profound
transformation during the 1990s. Many sectors of the energy industry have been
deregulated with competitive forces reaching down to the retail level. The
growth of trading volumes was accompanied by emergence of new types of energy
companies, specializing not so much in exploration, production and processing
of energy commodities, but in management of risks related to price volatility,
credit exposures and operations of physical assets. Significant percentage of
transactions was shifted from the organized exchanges and traditional OTC
markets to electronic trading platforms. This process came to an abrupt halt in
the United States, with unprecedented volatility of electricity and natural gas
prices in the western markets, followed by elimination or significant
retrenchment of major players. The questions I shall attempt to address are:
1. What are the underlying causes of the present crisis?
2. Can the energy markets be revitalized by the return of more disciplined
financial institutions to the energy markets?
3. Are energy markets (or certain segments of the energy complex) so unique
that a return to a system of resource allocation based on regulation is
4. What contribution can be made by the academic community to support
development of competitive energy markets?
Probabilistic Aspects of Portfolio Analysis and Optimization
Ioannis Karatzas, Robert Fernholz
We discuss the concept of "diversity" for a financial market, which means roughly that no single asset is allowed to dominate the entire market in terms of relative capitalization. In the context of the standard Ito-process model initiated by Samuelson, we formulate this property in precise terms and show that diversity is indeed possible, though rather delicate, to achieve. We provide examples demonstrating that diverse financial markets contain arbitrage opportunities, over sufficiently long time-horizons.
Towards a self-consistent theory of stochastic volatility
We study the influence of hedging over volatility. In aprticular we consider the case of a large investor and obtain some formulas for the liquidation values and option prices. From this analysis, we deduce a tentative self-consistent theory for volatility and we show that the corresponding mathematical problem is well-posed .
A valuation algorithm for incomplete models
Marek Musiela, Thaleia Zariphopoulou
The classical arbitrage pricing is based upon the concept of risk replication. One makes investment allocations in order to dynamically replicate future liability. Unfortunately, this pricing mechanism breaks down in incomplete models because one cannot offset all risk by taking positions in the market. We analyze the notion of value based upon the concept of optimal investment. The price corresponds to the amount which makes an investor indifferent to the various investment opportunities. The resulting valuation algorithm seems to be intuitively obvious. For each time period, one should condition the total risk at the end on the hedgeable one in order to extract the risk that cannot be hedged. Then, price that risk by certainty equivalent, and in the second step, price the remaining hedgeable risk by arbitrage. This defines the total risk at the beginning of the period and the valuation algorithm may be repeated.
Microstructure and Asset Pricing
Maureen O'Hara, David Easley
Market microstructure analyzes the behavior and formation of prices in asset markets. Fundamental to this approach is the belief that features of the particular trading mechanisms used in markets are important in influencing the behavior of asset prices. The asset pricing literature also considers the behavior and formation of asset prices. This literature focuses on linking asset price dynamics to underlying economic fundamentals. While these two literatures share a common focus, they also share a common flaw: neither literature explicitly recognizes the importance and role of the factors so crucial to the other approach. Given the central importance of asset pricing in finance, a junction of these two very important literatures would seem beneficial.
In this article, we seek to foster this process by surveying the work linking microstructure factors to asset price dynamics. In the short run, these asset price dynamics involve issues such as the auto-correlation and cross-correlation structure of stocks, and we examine the literature relating these correlation structures to microstructure factors such as non-synchronous trading and dealer behavior. In the longer run, issues such as liquidity and the relation of private information to asset price dynamics dominate the research agenda. We survey the theoretical work linking microstructure factors to long run returns, and we review the empirical literature. Our goal is to highlight what is known and not known about the effect of microstructure variables on short-run and long-run asset price behavior. We also summarize what issues remain contentious, and suggest guidance for future research.
The Fundamental Theorem of Asset Pricing under Proportional Transaction Costs in Finite Discrete Time
We prove a version of the Fundamental Theorem of Asset Pricing, which applies to Kabanov's approach to foreign exchange markets under transaction costs. The financial market is modelled by a dxd matrix-valued stochastic process specifying the mutual bid and ask prices between d assets.
We introduce the notion of "robust no arbitrage", which is a version of the no arbitrage concept, robust with respect to small changes of the bid ask spreads. Dually, we interpret a concept used by Kabanov and his co-authors as "strictly consistent price systems". We show that this concept extends the notion of equivalent martingale measures, playing a well-known role in the frictionless case, to the present setting of bid-ask processes.
The main theorem states that the bid-ask process satisfies the robust no arbitrage condition iff it admits a strictly consistent pricing system. This result extends the theorems of Harrison-Pliska and Dalang-Morton-Willinger to the present setting, and also generalizes previous results obtained by Kabanov, Rasonyi and Stricker.
An example of a 5x5-dimensional process shows that, in this theorem, the robust no arbitrage condition cannot be replaced by the so-called strict no arbitrage condition, thus answering negatively a question raised by Kabanov, Rasonyi and Stricker.
The Market Prices of Risks in Fixed Income Markets
Kenneth Singleton, Qiang Dai
This talk surveys the theoretical specifications of the market prices of factor risks (MPRs)in dynamic term structure models (DTSMs), and explores in depth the empirical implications of alternative specifications. Particular attention is given to how the choice of MPRs affects a DTSM's ability to match the conditional means and variances of excess returns on bonds. Additionally, we decompose the effects of the risk factors on bond yields into their effects on expected future short-term rates and market risk premiums. Finally, we relate the risk factors and the dynamic properties of the MPRs to macroeconomic developments.
Prices and Portfolio Choices in Financial Markets: Theory and Experimental Evidence
William Zame, Peter Bossaerts, Charles Plott
Almost all asset pricing theories make predictions about portfolio choices as well as about asset prices. However, most tests of asset pricing theories focus exclusively on the price predictions -- perhaps because the portfolio predictions are "obviously" wrong. This seems a paradox: how can the price predictions be right if the portfolio predictions on which they rest are wrong?
This work offers a model that resolves this paradox, experimental evidence consistent with the theoretical model, and econometric analysis that ties the two together.