A Discrete Time Equivalent Martingale Measure

An equivalent martingale measure selection strategy for discrete time, continuous state, asset price evolution models is proposed. The minimal martingale law is shown to generally fail to produce a probability law in this context. The proposed strategy, termed the extended Girsanov principle, performs a multiplicative decomposition of asset price movements into a predictable and martingale component with the measure change identifying the discounted asset price process to the martingale component. However, unlike the minimal martingale law, the resulting martingale law of the extended Girsanov principle leads to weak form efficient price processes. It is shown that the proposed measure change is relevant for economies in which investors adopt hedging strategies that minimize the variance of a risk adjusted discounted cost of hedging that uses risk adjusted asset prices in calculating hedging returns. Risk adjusted prices deflate asset prices by the asset's excess return. The explicit form of the change of measure density leads to tractable econometric strategies for testing the validity of the extended Girsanov principle. A number of interesting applications of the extended Girsanov principle are also developed.     

EQUILIBRIUM STATE PRICES IN A STOCHASTIC VOLATILITY MODEL1

In a stochastic volatility model, the no-free-lunch assumption does not induce a unique arbitrage price because of market incompleteness. In this paper, we consider a contingent claim on the primitive asset, traded in zero net supply. Given a system of Arrow-Debreu state prices, we provide necessary and sufficient conditions for consistency with an intertemporal additive equilibrium model that we fully characterize. We show that the risk premia corresponding to the minimal martingale of Föllmer and Schweizer (1991) are consistent with logarithmic preferences, while the Hull and White model (1987) (volatility risk premium independent of the asset price) is consistent with a class of utility functions including constant relative risk aversion (CRRA) ones.     

ASSET PRICES,OUTPUT AND MONETARY POLICY IN A SMALL OPEN ECONOMY

We formulate a macro‐model of a small open economy in order to investigate the relative performance of rules that respond to asset prices and those that do not. Our model consists of three asset prices: the stock price, the long‐term interest rate and the exchange rate. These asset prices interact with nominal wage and price Phillips curves, a law of motion for the labour share, a dynamic IS curve that describes output adjustment and a Taylor‐type interest rate policy rule. Estimations of the model show that policy rules that respond to asset price movements dominate rules that do not.     

Global excess liquidity and asset prices in emerging countries: A PVAR approach

The overly accommodating monetary policy is often accused of creating surplus liquidity and bubbles on the asset markets. In particular, it could have contributed to strong capital inflows in emerging countries, which may have had a significant impact on financial stability in these countries, affecting domestic financing conditions and creating a risk of upward pressures on asset prices. We focus in this paper on the impact of global excess liquidity on goods and asset prices for a set of emerging market countries by estimating a panel VAR model. We define first global liquidity and highlight situations of excess liquidity. We then find that excess liquidity at global level has spillover effects on output and price levels in emerging countries. The impact on real estate, commodity and share prices in emerging countries is less clear.     

我国房地产价格与通货膨胀关系的实证分析

近年来,我国房地产等资产的价格高涨所引起的“资产泡沫型通货膨胀”现象比较明显。通过观察我国近年来房屋销售价格指数和居民消费价格指数的走势发现,房地产高涨与通货膨胀之间具有很大的联动作用。因此,研究房地产价格与通货膨胀的关系,寻找破解房地产价格高涨、缓解通货膨胀压力的方法,具有重要的学术研究价值和现实意义。本文利用Granger因果关系检验模型,验证了我国房地产价格与通货膨胀关系之间存在Granger因果关系,并围绕高房价是怎样影响通货膨胀的逻辑思路,提出破解高房价、缓解“资产泡沫型通货膨胀”压力的解决方法。     

Semistatic hedging and pricing American floating strike lookback options

We price an American floating strike lookback option under the Black–Scholes model with a hypothetic static hedging portfolio (HSHP) composed of nontradable European options. Our approach is more efficient than the tree methods because recalculating the option prices is much quicker. Applying put–call duality to an HSHP yields a tradable semistatic hedging portfolio (SSHP). Numerical results indicate that an SSHP has better hedging performance than a delta-hedged portfolio. Finally, we investigate the model risk for SSHP under a stochastic volatility assumption and find that the model risk is related to the correlation between asset price and volatility.     

ASSET PRICE BUBBLES IN INCOMPLETE MARKETS*

This paper studies asset price bubbles in a continuous time model using the local martingale framework. Providing careful definitions of the asset's market and fundamental price, we characterize all possible price bubbles in an incomplete market satisfying the “no free lunch with vanishing risk (NFLVR)” and “no dominance” assumptions. We show that the two leading models for bubbles as either charges or as strict local martingales, respectively, are equivalent. We propose a new theory for bubble birth that involves a nontrivial modification of the classical martingale pricing framework. This modification involves the market exhibiting different local martingale measures across time—a possibility not previously explored within the classical theory. Finally, we investigate the pricing of derivative securities in the presence of asset price bubbles, and we show that: (i) European put options can have no bubbles; (ii) European call options and discounted forward prices have bubbles whose magnitudes are related to the asset's price bubble; (iii) with no dividends, American call options are not exercised early; (iv) European put‐call parity in market prices must always hold, regardless of bubbles; and (v) futures price bubbles can exist and they are independent of the underlying asset's price bubble. Many of these results stand in contrast to those of the classical theory. We propose, but do not implement, some new tests for the existence of asset price bubbles using derivative securities.     

CONTINGENT CLAIMS VALUED AND HEDGED BY PRICING AND INVESTING IN A BASIS

Contingent claims with payoffs depending on finitely many asset prices are modeled as elements of a separable Hilbert space. Under fairly general conditions, including market completeness, it is shown that one may change measure to a reference measure under which asset prices are Gaussian and for which the family of Hermite polynomials serves as an orthonormal basis. Basis pricing synthesizes claim valuation and basis investment provides static hedging opportunities. For claims written as functions of a single asset price we infer from observed option prices the implicit prices of basis elements and use these to construct the implied equivalent martingale measure density with respect to the reference measure, which in this case is the Black-Scholes geometric Brownian motion model. Data on S & P 500 options from the Wall Street Journal are used to illustrate the calculations involved. On this illustrative data set the equivalent martingale measure deviates from the Black-Scholes model by relatively discounting the larger price movements with a compensating premia placed on the smaller movements.     

Risk Minimization with Incomplete Information in a Model for High‐Frequency Data

We study risk‐minimizing hedging‐strategies for derivatives in a model where the asset price follows a marked point process with stochastic jump‐intensity, which depends on some unobservable state‐variable process. This model reflects stylized facts that are typical for high frequency data. We assume that agents in our model are restricted to observing past asset prices. This poses some problems for the computation of risk‐minimizing hedging strategies as the current value of the state variable is unobservable for our agents. We overcome this difficulty by a two‐step procedure, which is based on a projection result of Schweizer and show that in our context the computation of risk‐minimizing strategies leads to a filtering problem that has received some attention in the nonlinear filtering literature.     

Exchange risk and asset returns: A theoretical and empirical study of an open economy asset pricing model

This study develops a consumption-based asset pricing model in which domestic consumers can buy goods from domestic and foreign markets but can only invest in domestic markets. In this model, the exchange rate influences asset prices through the marginal utility of consumption and increases the risks investors face. We find that our model can successfully price the 25 Fama–French portfolios and industry portfolios in the Chinese market, and the exchange rate is an important pricing factor in the unconditional linear model. We also find that the exchange risk is time-varying and countercyclical, which can help to explain the countercyclicality in equity premium.     

ANALYTIC APPROXIMATIONS FOR MULTI‐ASSET OPTION PRICING

We derive general analytic approximations for pricing European basket and rainbow options on N assets. The key idea is to express the option’s price as a sum of prices of various compound exchange options, each with different pairs of subordinate multi‐ or single‐asset options. The underlying asset prices are assumed to follow lognormal processes, although our results can be extended to certain other price processes for the underlying. For some multi‐asset options a strong condition holds, whereby each compound exchange option is equivalent to a standard single‐asset option under a modified measure, and in such cases an almost exact analytic price exists. More generally, approximate analytic prices for multi‐asset options are derived using a weak lognormality condition, where the approximation stems from making constant volatility assumptions on the price processes that drive the prices of the subordinate basket options. The analytic formulae for multi‐asset option prices, and their Greeks, are defined in a recursive framework. For instance, the option delta is defined in terms of the delta relative to subordinate multi‐asset options, and the deltas of these subordinate options with respect to the underlying assets. Simulations test the accuracy of our approximations, given some assumed values for the asset volatilities and correlations. Finally, a calibration algorithm is proposed and illustrated.     

银行信贷和资产价格泡沫的联动性——基于动态贷款价值比的分析

投资者借贷投资是现代金融市场的常态。信息不对称及其带来的风险收益不对称和风险转移问题,会造成资产价格泡沫。文章引入贷款价值比进一步扩展了Allen-Gale模型,并用贷款价值比的动态变化来说明资产价格泡沫生成的内在机理及其所产生的影响;通过对贷款价值比动态调整的模拟得出:贷款价值比越大,资产价格泡沫越大。因此,降低贷款价值比是遏制资产价格泡沫膨胀的关键。     

Analysis of Bitcoin prices using market and sentiment variables

This paper proposes an empirical model for analysing the dynamics of Bitcoin prices. To do this, we consider a vector error correction model over two overlapping periods: 2010–17 and 2010–19. Price discovery is achieved through the Gonzalo–Granger permanent‐transitory decomposition. The pricing factors are endogenous linear combinations of the S&P 500 index, gold price, a Google search variable associated to Bitcoin and a fear index proxied by the FED Financial Stress Index. Our empirical analysis shows that during the first period, a linear combination of four pricing factors describes the efficient Bitcoin price. The S&P 500 index and Google searches have a positive effect whereas gold prices and the fear index have a negative effect. In contrast, during the second period, the efficient price behaves idiosyncratically and can be only rationalised by individuals' search for information on the cryptocurrency. These findings provide empirical evidence on the presence of a correction in Bitcoin prices during the period 2018–19 uncorrelated to market fundamentals. We also show that standard empirical asset pricing models perform poorly for explaining Bitcoin prices.     

AN EQUILIBRIUM GUIDE TO DESIGNING AFFINE PRICING MODELS

The paper examines equilibrium models based on Epstein–Zin preferences in a framework in which exogenous state variables follow affine jump diffusion processes. A main insight is that the equilibrium asset prices can be computed using a standard machinery of affine asset pricing theory by imposing parametric restrictions on market prices of risk, determined inside the model by preference and model parameters. An appealing characteristic of the general equilibrium setup is that the state variables have an intuitive and testable interpretation as driving the consumption and dividend dynamics. We present a detailed example where large shocks (jumps) in consumption volatility translate into negative jumps in equilibrium prices of the assets as agents demand a higher premium to compensate for higher risks. This endogenous “leverage effect,” which is purely an equilibrium outcome in the economy, leads to significant premiums for out‐of‐the‐money put options. Our model is thus able to produce an equilibrium “volatility smirk,” which realistically mimics that observed for index options.     

Hedging multiple price and quantity exposures

We examined the general hedging problem faced by a global portfolio manager or a pure exporting multinational firm. Most hedging models assume that these economic agents hold only a single asset in the spot market and are exposed only to a single source of price–quantity uncertainty. Such models are less relevant to many financial and exporting firms that face multiple sources of risk. In this study, we developed a general hedging model that explicitly recognizes that these hedgers are faced with multiple price and quantity uncertainties. Our model takes advantage of the full correlation structure of changes in spot prices, quantities, and forward prices. We performed simulations of the hedging model for a firm with two pairs of price and quantity exposures to demonstrate potential gains in hedging efficiency and effectiveness. © 2001 John Wiley & Sons, Inc. Jrl Fut Mark 21:145–172, 2001     

An explicitly solvable multi‐scale stochastic volatility model: Option pricing and calibration problems

We introduce an explicitly solvable multiscale stochastic volatility model that generalizes the Heston model. The model describes the dynamics of an asset price and of its two stochastic variances using a system of three Ito stochastic differential equations. The two stochastic variances vary on two distinct time scales and can be regarded as auxiliary variables introduced to model the dynamics of the asset price. Under some assumptions, the transition probability density function of the stochastic process solution of the model is represented as a one‐dimensional integral of an explicitly known integrand. In this sense the model is explicitly solvable. We consider the risk‐neutral measure associated with the proposed multiscale stochastic volatility model and derive formulae to price European vanilla options (call and put) in the multiscale stochastic volatility model considered. We use the thus‐obtained option price formulae to study the calibration problem, that is to study the values of the model parameters, the correlation coefficients of the Wiener processes defining the model, and the initial stochastic variances implied by the “observed” option prices using both synthetic and real data. In the analysis of real data, we use the S&P 500 index and to the prices of the corresponding options in the year 2005. The web site http://www.econ.univpm.it/recchioni/finance/w7 contains some auxiliary material including some animations that helps the understanding of this article. A more general reference to the work of the authors and their coauthors in mathematical finance is the web site http://www.econ.univpm.it/recchioni/finance . © 2009 Wiley Periodicals, Inc. Jrl Fut Mark 29:862–893, 2009     

Contingent Claims and Market Completeness in a Stochastic Volatility Model

In an incomplete market framework, contingent claims are of particular interest since they improve the market efficiency. This paper addresses the problem of market completeness when trading in contingent claims is allowed. We extend recent results by Bajeux and Rochet (1996) in a stochastic volatility model to the case where the asset price and its volatility variations are correlated. We also relate the ability of a given contingent claim to complete the market to the convexity of its price function in the current asset price. This allows us to state our results for general contingent claims by examining the convexity of their "admissible arbitrage prices."     

汇率预期对中国通货膨胀影响的实证研究

汇率预期主要通过货币替代效应、资产价格效应和进口价格效应影响物价水平。递归VAR模型检验结果表明:2002年以来的人民币升值预期对本轮通货膨胀影响显著,其中,资产价格效应、货币替代效应、进口价格效应依次增强,影响主要集中在前期;同时,汇率预期变量对工业品出厂价格指数、消费者价格指数及货币供应量的影响都十分明显。     

INDIFFERENCE PRICES AND IMPLIED VOLATILITIES

We consider a general local‐stochastic volatility model and an investor with exponential utility. For a European‐style contingent claim, whose payoff may depend on either a traded or nontraded asset, we derive an explicit approximation for both the buyer's and seller's indifference prices. For European calls on a traded asset, we translate indifference prices into an explicit approximation of the buyer's and seller's implied volatility surfaces. For European claims on a nontraded asset, we establish rigorous error bounds for the indifference price approximation. Finally, we implement our indifference price and implied volatility approximations in two examples.     

Hedging under the influence of transaction costs: An empirical investigation on FTSE 100 index options

The Black–Scholes (BS; F. Black & M. Scholes, 1973) option pricing model, and modern parametric option pricing models in general, assume that a single unique price for the underlying instrument exists, and that it is the mid‐ (the average of the ask and the bid) price. In this article the authors consider the Financial Times and London Stock Exchange (FTSE) 100 Index Options for the time period 1992–1997. They estimate the ask and bid prices for the index, and show that, when substituted for the mid‐price in the BS formula, they provide superior option price predictors, for call and put options, respectively. This result is reinforced further when they .t a non‐parametric neural network model to market prices of liquid options. The empirical .ndings in this article suggest that the ask and bid prices of the underlying asset provide a superior fit to the mid/closing price because they include market maker's, compensation for providing liquidity in the market for constituent stocks of the FTSE 100 index. © 2007 Wiley Periodicals, Inc. Jrl Fut Mark 27:471–494, 2007