Private Information in Sequential Common-Value Auctions

We study an infinitely-repeated ?rst-price auction with common values. Initially, bid- ders receive independent private signals about the objects' value, which itself does not change over time. Learning occurs only through observation of the bids. Under one-sided incomplete information, this information is eventually revealed and the seller extracts es- sentially the entire rent (for large discount factors). Both players?payo¤s tend to zero as the discount factor tends to one. However, the uninformed bidder does relatively better than the informed bidder. We discuss the case of two-sided incomplete information, and argue that, under a Markovian re?nement, the outcome is pooling: information is revealed only insofar as it does not affect prices. Bidders submit a common, low bid in the tradition of collusion without conspiracy.repeated game with incomplete information; private information; ratchet effect; first-price auction; dynamic auctions

A Maximum Likelihood Approach to Estimation of Heath-Jarrow-Morton Models

Research on the Heath-Jarrow-Morton (1992) term structure models so far has focused on the class having time-deterministic instantaneous forward rate volatility. In this case the forward rate is Markovian, even if the spot rate process is not. However, this Markovian feature can only be used under the historical measure, involving two unsatisfactory assumptions: one on market price risk, usually made for pure mathematical tractability, the other to use futures yields as a proxy for the instantaneous forward rate, which may result in estimation bias. This paper circumvents both of these assumptions. First, the bias is quantified and shown to be non-negligible. Then futures contracts are treated as derivative instruments written on forward rates to derive the full information maximum likelihood estimator for observable futures prices, using both time series and cross-sectional data, without the need to assume and estimate any functional forms for the market price of interest rate risk. The derivation involves the likelihood transformation method of Duan (1994). The method is then applied to the estimation of a humped forward rate volatility model for Eurodollar futures series traded on the Chicago Mercantile Exchange.term structure; heath-jarrow-morton; time-deterministic forward volatility; humped forward volatility model; full information maximum likelihood

A Benchmark Approach to Risk-Minimization under Partial Information

In this paper we study a risk-minimizing hedging problem for a semimartingale incomplete financial market where d+1 assets are traded continuously and whose price is expressed in units of the num\'{e}raire portfolio. According to the so-called benchmark approach, we investigate the (benchmarked) risk-minimizing strategy in the case where there are restrictions on the available information. More precisely, we characterize the optimal strategy as the integrand appearing in the Galtchouk-Kunita-Watanabe decomposition of the benchmarked claim under partial information and provide its description in terms of the integrands in the classical Galtchouk-Kunita-Watanabe decomposition under full information via dual predictable projections. Finally, we apply the results in the case of a Markovian jump-diffusion driven market model where the assets prices dynamics depend on a stochastic factor which is not observable by investors.Comment: 31 page

Pricing options and equity-indexed annuities in a regime-switching model by trinomial tree method

In this paper we summarize the main idea and results of Yuen and Yang (2009, 2010a, 2010b). The Markov regime-switching model (MRSM) has recently become a popular model. The MRSM allows the parameters of the market model depending on a Markovian process, and the model can reflect the information of the market environment which cannot be modeled solely by linear Gaussian process. The Markovian process can ensure that the parameters change according to the market environment and at the same time preserves the simplicity of the model. It is also consistent with the efficient market hypothesis that all the effects of the information about the stock price would reflect on the stock price. However, when the parameters of the stock price model are not constant but governed by a Markovian process, the pricing of the options becomes complex. We present a fast and simple trinomial tree model to price options in MRSM. In recent years, the pricing of modern insurance products, such as Equity-Indexed annuity (EIA) and variable annuities (VAs), has become a popular topic. These products can be considered investment plans with associated life insurance benefits, a specified benchmark return, a guarantee of an annual minimum rate of return and a specified rule of the distribution of annual excess investment return above the guaranteed return. EIA usually has a long maturity time, hence it is not appropriate to assume that the interest rate and the volatility of the equity index are constants. One way to deal with this problem is to apply the regime switching model. However, the valuation of derivatives in such model is challenging when the number of states are large, especially for the strong path dependent options such as Asian options. Our trinomial tree model provides an efficient way to solve this problem.postprintThe 5th Oxford-Princeton Workshop on Financial Mathematics & Stochastic Analysis, Princeton, N.J., 27-28 March 2009

Quantum Brownian motion model for the stock market

It is believed by the majority today that the efficient market hypothesis is imperfect because of market irrationality. Using the physical concepts and mathematical structures of quantum mechanics, we construct an econophysics framework for the stock market, based on which we analogously map massive numbers of single stocks into a reservoir consisting of many quantum harmonic oscillators and their stock index into a typical quantum open system--a quantum Brownian particle. In particular, the irrationality of stock transactions is quantitatively considered as the Planck constant within Heisenberg's uncertainty relationship of quantum mechanics in an analogous manner. We analyze real stock data of Shanghai Stock Exchange of China and investigate fat-tail phenomena and non-Markovian behaviors of the stock index with the assistance of the quantum Brownian motion model, thereby interpreting and studying the limitations of the classical Brownian motion model for the efficient market hypothesis from a new perspective of quantum open system dynamics

Price dynamics in a Markovian limit order market

We propose and study a simple stochastic model for the dynamics of a limit order book, in which arrivals of market order, limit orders and order cancellations are described in terms of a Markovian queueing system. Through its analytical tractability, the model allows to obtain analytical expressions for various quantities of interest such as the distribution of the duration between price changes, the distribution and autocorrelation of price changes, and the probability of an upward move in the price, {\it conditional} on the state of the order book. We study the diffusion limit of the price process and express the volatility of price changes in terms of parameters describing the arrival rates of buy and sell orders and cancelations. These analytical results provide some insight into the relation between order flow and price dynamics in order-driven markets.Comment: 18 pages, 5 figure

Markovian approximation in foreign exchange markets

In this paper we test the random walk hypothesis on the high frequency dataset of the bid--ask Deutschemark/US dollar exchange rate quotes registered by the inter-bank Reuters network over the period October 1, 1992 to September 30, 1993. Then we propose a stochastic model for price variation which is able to describe some important features of the exchange market behavior. Besides the usual correlation analysis we have verified the validity of this model by means of other approaches inspired by information theory . These techniques are not only severe tests of the approximation but also evidence some aspects of the data series which have a clear financial relevance.Comment: 19 pages, LaTeX, uses elsart.cls and JournalOfFinance.sty, 7 eps figures, submitted to J. of Int. Money and Financ