Testing the martingale hypothesis in deutsche mark futures with models specifying the form of heteroscedasticity

We examine the form of heteroscedasticity in Deutsche Mark futures price data and compare different specifications of the particular way that the variance is changing over time. The martingale hypothesis is tested with daily and weekly rates of change of futures prices for the Deutsche Mark and some evidence is found against this hypothesis in analyses of daily data from 1981 to 1985. This rejection of the martingale hypothesis may be attributed to trading day effects in foreign currency prices and the resulting day-of-the-week patterns in futures prices. When the martingale hypothesis is tested with weekly data the null hypothesis is retained.     

Applications of the Likelihood Theory in Finance: Modelling and Pricing

This paper discusses the connection between mathematical finance and statistical modelling which turns out to be more than a formal mathematical correspondence. We like to figure out how common results and notions in statistics and their meaning can be translated to the world of mathematical finance and vice versa. A lot of similarities can be expressed in terms of LeCam’s theory for statistical experiments which is the theory of the behaviour of likelihood processes. For positive prices the arbitrage free financial assets fit into statistical experiments. It is shown that they are given by filtered likelihood ratio processes. From the statistical point of view, martingale measures, completeness, and pricing formulas are revisited. The pricing formulas for various options are connected with the power functions of tests. For instance the Black–Scholes price of a European option is related to Neyman–Pearson tests and it has an interpretation as Bayes risk. Under contiguity the convergence of financial experiments and option prices are obtained. In particular, the approximation of Itô type price processes by discrete models and the convergence of associated option prices is studied. The result relies on the central limit theorem for statistical experiments, which is well known in statistics in connection with local asymptotic normal (LAN) families. As application certain continuous time option prices can be approximated by related discrete time pricing formulas.     

Bounds for the utility-indifference prices of non-traded assets in incomplete markets

Abstract We consider a special class of financial models with both traded and non-traded assets and show that the utility indifference (bid) price of a contingent claim on a non-traded asset is bounded above by the expectation under the minimal martingale measure. This bound also represents the marginal bid price for the claim. The key conclusion is that the bound and the marginal bid price are independent of both the utility function and initial wealth of the agent. Thus all utility maximising agents charge the same marginal price for the claim. This conclusion is in some sense the opposite conclusion to that of Hubalek and Schachermayer (2001), who show that any price is consistent with some equivalent martingale measure. Mathematics Subject Classification (2000): 91B28, 91B16, 60J70 Journal of Economic Literature Classification: G13     

On pricing and hedging options in regime-switching models with feedback effect

We study the pricing and hedging of European-style derivative securities in a Markov, regime-switching, model with a feedback effect depending on the economic condition. We adopt a pricing kernel which prices both financial and economic risks explicitly in a dynamically incomplete market and we provide an equilibrium analysis. A martingale representation for a European-style index option's price is established based on the price kernel. The martingale representation is then used to construct the local risk-minimizing strategy explicitly and to characterize the corresponding pricing measure.     

Detecting Financial Collapse and Ballooning Sovereign Risk

This paper proposes a new model for capturing discontinuities in the underlying financial environment that can lead to abrupt falls, but not necessarily sustained monotonic falls, in asset prices. This notion of price dynamics is consistent with existing understanding of market crashes, which allows for a mix of market responses that are not universally negative. The model may be interpreted as a martingale composed with a randomized drift process that is designed to capture various asymmetric drivers of market sentiment. In particular, the model is capable of generating realistic patterns of price meltdowns and bond yield inflations that constitute major market reversals while not necessarily being always monotonic in form. The recursive and moving window methods developed in Phillips, Shi and Yu (2015a,b; PSY), which were designed to detect exuberance in financial and economic data, are shown to have detective capacity for such meltdowns and expansions. This characteristic of the PSY tests has been noted in earlier empirical studies by the present authors and other researchers but no analytic reasoning has yet been given to explain why methods intended to capture the expansionary phase of a bubble may also detect abrupt and broadly sustained collapses. The model and asymptotic theory developed in the present paper together explain this property of the PSY procedures. The methods are applied to analyse S&P 500 stock prices and sovereign risk in European Union countries over 2001–16 using government bond yields and credit default swap (CDS) premia. A pseudo real‐time empirical analysis of these data shows the effectiveness of the monitoring strategy in capturing key events and turning points in market risk assessment.     

Equal risk pricing under convex trading constraints

In an incomplete market model where convex trading constraints are imposed upon the underlying assets, it is no longer possible to obtain unique arbitrage-free prices for derivatives using standard replication arguments. Most existing derivative pricing approaches involve the selection of a suitable martingale measure or the optimisation of utility functions as well as risk measures from the perspective of a single trader.We propose a new and effective derivative pricing method, referred to as the equal risk pricing approach, for markets with convex trading constraints. The approach analyses the risk exposure of both the buyer and seller of the derivative, and seeks an equal risk price which evenly distributes the expected loss for both parties under optimal hedging. The existence and uniqueness of the equal risk price are established for both European and American options. Furthermore, if the trading constraints are removed, the equal risk price agrees with the standard arbitrage-free price.Finally, the equal risk pricing approach is applied to a constrained Black–Scholes market model where short-selling is banned. In particular, simple pricing formulas are derived for European calls, European puts and American puts.     

Non-transferable non-hedgeable executive stock option pricing

To value non-transferable non-hedgeable (NTNH) contingent claims and price executive stock options (ESOs), we use a replication argument to translate portfolios with NTNH derivatives into portfolios of primary assets (only) with stochastic portfolio constraints. By identifying stochastic discount factors and finding subjective prices of NTNH European and American ESOs, for block and continuous partial exercise, we derive executives׳ optimal exercise policies, and use these to find objective prices/costs of ESOs to firms. Through numerical simulations, we obtain policy implications regarding ESOs׳ incentivizing efficiency. For the first time, we demonstrate that, unlike under block exercise, subjective prices under continuous partial exercise may be higher than objective ones. Moreover, volatility regimes and executives׳ “other wealth” are important in ESO pricing, and are thus essential to empirical executive compensation studies.     

Bid-ask dynamic pricing in financial markets with transaction costs and liquidity risk

According to the classic no arbitrage theory of asset pricing, in a frictionless market a No Free Lunch dynamic price process associated with any essentially bounded asset is a martingale under an equivalent probability measure. However, real financial markets are not frictionless. We introduce an axiomatic approach of Time Consistent Pricing Procedure (TCPP), in a model free setting, to assign to every financial position a dynamic ask (resp. bid) price process. Taking into account both transaction costs and liquidity risk this leads to the convexity (resp. concavity) of the ask (resp. bid) price. We prove that the No Free Lunch condition for a TCPP is equivalent to the existence of an equivalent probability measure R that transforms a process between the bid price process and the ask price process of every financial instrument into a martingale. Furthermore we prove that the ask (resp. bid) price process associated with every financial instrument is then a R super-martingale (resp. R sub-martingale) which has a càdlàg version.     

Price-matching policies: An empirical case

Promises by retailers to match the prices of their competitors give an impression of fierce price competition. These policies, however, may deter rivals from cutting prices because the threat of price matching makes it more likely that market share will not be gained. This paper empirically tests these two conflicting theories using data collected from grocery stores in a market where several stores had announced that they would match the prices of the low-price supermarket. The evidence supports the theory that price-matching policies help supermarkets avoid price competition and therefore lead to generally higher prices.     

Pricing vulnerable options with stochastic liquidity risk

In this paper, we consider vulnerable options with stochastic liquidity risk. We employ liquidity-adjusted pricing models to describe the underlying stock price and option issuer’s assets. In addition, the correlation between these assets is stochastic, depending on the market liquidity measures. In the proposed framework, we derive closed forms of vulnerable European options with stochastic liquidity risk and then use them to illustrate the effects of stochastic liquidity risk on vulnerable option prices. Numerical results show that the effects of liquidity risk on the prices of out-of-the-money options or the options with a short maturity are not negligible.     

Consumer Cognition and Pricing in the Nines in Oligopolistic Markets

The paper fully characterizes the Bertrand equilibria of oligopolistic markets where consumers may ignore the last (i.e., the right-most) digits of prices. Consumers, in this model, do not do this reflexively or out of irrationality, but only when they expect the time cost of acquiring full cognizance of the exact price to exceed the expected loss caused by the slightly erroneous amounts that are likely to be purchased or the slightly higher price that may be paid by virtue of ignoring the information concerning the last digits of prices. It is shown that in this setting there will always exist firms that set prices that end in nine though there may also be some (nonstrict) equilibria where a non-nine price ending occurs. It is shown that all firms earn positive profits even in Bertrand equilibria. The model helps us understand in what kinds of markets we are most likely to encounter pricing in the nines.     

A model of international asset pricing under imperfect commodity arbitrage

This paper examines the effect of imperfect international commodity arbitrage (i.e., violation of the law of one price), modeled as the existence of non-traded goods, on the structure of purchasing power risk, optimal portfolio rules of the risk-averse investors and the equilibrium yield relationship among assets. The major results of the paper include: (i) There are two separate sources of purchasing power risk, i.e., relative price risk and inflation risk; relative price risk is specific to the country in which the investor resides. (ii) In a world of n countries, investors may hold n + 1 hedge portfolios as vehicles to hedge against purchasing power risk; facing different relative prices, investors residing in different countries display divergent portfolio behavior. (iii) In equilibrium, investors are compensated in terms of excess return for bearing not only the systematic world market risk but also the systematic inflation and relative price risks.     

对上证指数波动性的实证分析

股票价格频繁波动是股票市场中最明显的特征之一。ARCH类模型可以成功的预测金融资产收益的方差。通过对我国股价指数的统计描述,表明我国金融资产收益率存在自回归条件异方差,并表现出非正态性。并且应用GARCH、TARCH、EGARCH模型理论,进一步分析了日收益率波动的条件异方差性、非对称性。     

Competitive market equilibrium under asymmetric information

This paper studies the existence of a competitive market equilibrium under asymmetric information. There are two agents involved in the trading of the risky assets: an “informed” trader and an “ordinary” trader. The market is competitive and the ordinary agent can infer the insider information from the price dynamics of the risky assets. The insider information is considered to be the total supply of the risky assets. The definition of market equilibrium is based on the law of supply-demand as described by a rational expectations equilibrium of the Grossman and Stiglitz (Am Econ Rev 70:393–408, 1980) model. We show that equilibrium can be attained by linear dynamics of an admissible price process of the risky assets for a given linear supply dynamics.      

Leverage and the price volatility of equity shares in equilibrium

The traditional valuation formulas for corporate debt, which are derived in a complete market setting and are based on the no-arbitrage principle, imply that equity prices become more volatile as leverage increases. If the asset structure is incomplete, the presence of corporate debt affects the linear subspace spanned by the payoffs of the existing assets, and the pricing of corporate debt and shares of levered firms becomes a simultaneous valuation problem. This paper characterizes the relationship between the price of corporate debt and the share price of a levered firm in an equilibrium framework where corporate debt is a non-redundant asset. While, in the absence of bankruptcy, higher leverage always implies riskier equity, it does not necessarily mean more volatile equity prices. In fact, the link between leverage and equity price volatility depends in a particular way on investors’ preferences towards risk.     

Stocks,bonds, money markets and exchange rates: measuring international financial transmission

Understanding the complexity of the financial transmission process across various assets—domestically as well as within and across asset classes—requires the simultaneous modeling of the various transmission channels in a single, comprehensive empirical framework. The paper estimates the financial transmission between money, bond and equity markets and exchange rates within and between the USA and the euro area. We find that asset prices react strongest to other domestic asset price shocks, but that there are also substantial international spillovers, both within and across asset classes. The results underline the dominance of US markets as the main driver of global financial markets: US financial markets explain, on average, around 30% of movements in euro area financial markets, whereas euro area markets account only for about 6% of US asset price changes. Moreover, the methodology allows us to identify indirect spillovers through other asset prices, which are found to increase substantially the international transmission of shocks within asset classes. Copyright © 2010 John Wiley & Sons, Ltd.     

Optimal time-consistent reinsurance and investment strategies for a jump–diffusion financial market without cash

This paper considers an optimal reinsurance and investment strategies for an insurer under mean–variance criterion within a game theoretic framework. Specially, it is assumed that the surplus process is governed by a Cramér–Lundberg model, and apart from purchasing reinsurance, the insurer is allowed to invest in a financial market with multiple assets that all can be risky, whose price processes are modeled by the jump–diffusion process. Due to the market without cash, the method of separating the variables is not viable any more. We turn to an alternative approach to solve the extended Hamilton–Jacobi–Bellman equation, and closed-form expressions of the optimal strategies and value function are not only derived but also proved to be uniqueness. Moreover, some special cases of our model are provided and several numerical analyses for our results are presented as well. Under this criterion, different from existing literature, we find that (i) the value function is not linear but quadratic with respect to the current wealth; (ii) the optimal reinsurance and investment strategies depend on the wealth process; (iii) the parameters of risky assets(insurance market) have impacts on the optimal reinsurance(investment) policy; (iv) the safety loading of the insurer affects the optimal strategies.     

Productivity,price recovery,capacity constraints and their financial consequences

Mining and fishing are both extractive industries, although one resource is renewable and the other is not. Miners and fishers pursue financial objectives, although their objectives may differ. In both industries financial performance is influenced by productivity and prices. Finally, in both industries capacity constraints influence financial performance, perhaps but not necessarily through their impact on productivity, and both industries encounter external as well as internal capacity constraints. In this study we develop an analytical framework that links all four phenomena. We use return on assets to measure financial performance, and our analytical framework is provided by the duPont triangle. We measure productivity change in two ways, with a theoretical technology-based index and with empirical price-based indexes. We measure price change with empirical quantity-based indexes. We measure internal capacity utilization by relating a pair of output quantity vectors representing actual output and full capacity output, and we develop physical and economic measures of internal capacity utilization. We also show how external capacity constraints can restrict the ability to reach full capacity output. The analytical framework has productivity change, price change and change in capacity utilization influencing change in return on assets.     

Corporate hedging and input price risk

Input price variability is an important source of risk for corporations that process raw commodities. Models of optimal input hedging are developed in this paper based on the maximization of managerial expected utility. The relationship between hedging strategies and output decisions is examined to assess the impact of the ability to set output prices on futures market participation. As a firm's ability to set output prices diminishes in the short run, input futures positions increase although the optimal hedge ratio may either increase or decrease. For a perfectly competitive firm, however, shifts in output price caused by input price changes provide a natural cash market hedge of input price risk and reduce the firm's optimal input futures position.     

The role of the list price in housing markets: Theory and an econometric model

Houses are routinely sold at prices below, but rarely sold at prices above, their list prices. List prices appear to be price ceilings that preclude the possibility of sales at higher prices. This paper presents a theory of sellers' behaviour that explains why there are list prices in housing markets and why list prices are distinct from sellers' reservation prices. The theory forms the basis of an econometric model that has been estimated using data from the Baltimore, MD, area. The estimated model predicts sale and reservation prices conditional on list prices. The predictions of sale prices are considerably more accurate than those obtained from a standard hedonic price regression. The estimated model also explains why sellers may not be willing to reduce their list prices even after their houses have remained unsold for long periods of time.