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.     

Corporate security prices in structural credit risk models with incomplete information

The paper studies derivative asset analysis in structural credit risk models where the asset value of the firm is not fully observable. It is shown that in order to determine the price dynamics of traded securities, one needs to solve a stochastic filtering problem for the asset value. We transform this problem to a filtering problem for a stopped diffusion process and apply results from the filtering literature to this problem. In this way, we obtain an stochastic partial differential equation characterization for the filter density. Moreover, we characterize the default intensity under incomplete information and determine the price dynamics of traded securities. Armed with these results, we study derivative assets in our setup: We explain how the model can be applied to the pricing of options on traded assets and we discuss dynamic hedging and model calibration. The paper closes with a small simulation study.     

CONSTANT PROPORTION PORTFOLIO INSURANCE IN THE PRESENCE OF JUMPS IN ASSET PRICES

Constant proportion portfolio insurance (CPPI) allows an investor to limit downside risk while retaining some upside potential by maintaining an exposure to risky assets equal to a constant multiple of the cushion , the difference between the current portfolio value and the guaranteed amount. Whereas in diffusion models with continuous trading, this strategy has no downside risk, in real markets this risk is nonnegligible and grows with the multiplier value. We study the behavior of CPPI strategies in models where the price of the underlying portfolio may experience downward jumps. Our framework leads to analytically tractable expressions for the probability of hitting the floor, the expected loss, and the distribution of losses. This allows to measure the gap risk but also leads to a criterion for adjusting the multiplier based on the investor's risk aversion. Finally, we study the problem of hedging the downside risk of a CPPI strategy using options. The results are applied to a jump-diffusion model with parameters estimated from returns series of various assets and indices.     

The Valuation Model for a Risky Asset When Its Risky Factors Follow Gamma Distributions

This paper constructed a pricing model for the asset with multi‐risks by specifying the risky factors (i.e., interest rate and termination hazard rates) to follow gamma distributions. The model not only avoids the possibility of the termination hazard rate taking an irrational (i.e., negative) value, but it also makes it easier to derive a valuation formula for a risky asset. Our model can also effortless apply because the parameters of the gamma distribution can easily be estimated from market data. An example using Taiwanese bond data illustrates how the model can be utilized for practical applications. To facilitate understanding of how accurately the different models price risky bonds, we compare their out‐of‐sample pricing errors for different hazard rate specifications assuming normal and gamma distributions. The results show that our pricing formula is realistic and accurate in its applications. Therefore, it should help market participants to accurately price risky assets and to effectively manage complicated portfolios.     

INVESTING WITH LIQUID AND ILLIQUID ASSETS

We find optimal trading policies for long‐term investors with constant relative risk aversion and constant investment opportunities, which include one safe asset, liquid risky assets, and an illiquid risky asset trading with proportional costs. Access to liquid assets creates a diversification motive, which reduces illiquid trading, and a hedging motive, which both reduces illiquid trading and increases liquid trading. A further tempering effect depresses the liquid asset's weight when the illiquid asset's weight is close to ideal, to keep it near that level by reducing its volatility. Multiple liquid assets lead to portfolio separation in four funds: the safe asset, the myopic portfolio, the illiquid asset, and its hedging portfolio.     

PORTFOLIO OPTIMIZATION WITH DOWNSIDE CONSTRAINTS

We consider the portfolio optimization problem for an investor whose consumption rate process and terminal wealth are subject to downside constraints. In the standard financial market model that consists of d risky assets and one riskless asset, we assume that the riskless asset earns a constant instantaneous rate of interest,   r > 0  , and that the risky assets are geometric Brownian motions. The optimal portfolio policy for a wide scale of utility functions is derived explicitly. The gradient operator and the Clark–Ocone formula in Malliavin calculus are used in the derivation of this policy. We show how Malliavin calculus approach can help us get around certain difficulties that arise in using the classical "delta hedging" approach.     

基于风险预算的新疆居民家庭金融资产的风险资产配置

通过对新疆2013-2017年的居民家庭金融总资产以及投资和储蓄的分析,从宏观的家庭金融资产视角使用Markowitz的投资组合的均值-方差模型在风算预算的基础上,进一步计算出实际新疆居民每年应当用于储蓄或者用于投资与固定风险和较大风险的比例,即得出风险资产的配置,从而提高新疆居民的储蓄向投资的转化,加强居民金融资产的管理和风险资产的分配,提高居民的风险收益,为新疆居民家庭获取更多金融资产投资于风险性收入提供更好的政策建议。     

ASSET DEMANDS AND SLUTSKY EQUATIONS WHEN ALL ASSETS ARE RISKY

This paper exploits the properties of the indirect expected utility function to explore the testable implications of a portfolio model in which all assets are risky. An uncertainty analogue of Roy's Identity and extremely simple derivations of Slutsky equations for risk and return are used in the analysis. Substitutability/complementarity relations between asset pairs are also explored. The one-riskless-asset case emerges as a special case of the present model, and it is shown that (since inflation uncertainty makes all real returns uncertain) the inclusion of a riskless asset would lead to misleading over-simplifications.     

保险资金投资管理中的风险分散问题研究

组合投资是利用投资组合内各个风险资产之间的相关性来分散风险的,而均值—方差投资组合模型采用的相关性度量—相关系数无法准确地度量风险资产之间的相关性,这必将对组合投资的风险分散效果产生不利影响。本文提出,用理论性质更好的相关性度量来度量风险资产之间的相关性,并建立基于Kendallτ的投资组合模型。通过实证研究发现,在保险资金投资管理中,采用基于Kendallτ的投资组合模型能够取得比均值—方差投资组合模型更好的风险分散效果。     

Pricing Options On Risky Assets In A Stochastic Interest Rate Economy1

This paper studies contingent claim valuation of risky assets in a stochastic interest rate economy. the model employed generalizes the approach utilized by Heath, Jarrow, and Morton (1992) by imbedding their stochastic interest rate economy into one containing an arbitrary number of additional risky assets. We derive closed form formulae for certain types of European options in this context, notably call and put options on risky assets, forward contracts, and futures contracts. We also value American contingent claims whose payoffs are permitted to be general functions of both the term structure and asset prices generalizing Bensoussan (1984) and Karatzas (1988) in this regard. Here, we provide an example where an American call's value is well defined, yet there does not exist an optimal trading strategy which attains this value. Furthermore, this example is not pathological as it is a generalization of Roll's (1977) formula for a call option on a stock that pays discrete dividends.     

A multivariate test of the covariance-co-skewness restriction for the three moment CAPM

This paper re-examines the importance of co-skewness in asset pricing using the multivariate testing procedure proposed by Gibbons (1982). This new approach allows for the testing of a share restriction derived from the Kraus and Litzenberger (1976) model which has been ignored in previous empirical studies. The results indicate that co-skewness is statistically significant in pricing risky assets and that the covariance risk is much more important in explaining the risk-return relationship than the co-skewness risk. However, the results also indicate that the Kraus and Litzenberger model does not adequately describe expected returns.     

Optimal investment and pricing in the presence of defaults

We consider the optimal investment problem with random endowment in the presence of defaults. For an investor with constant absolute risk aversion, we identify the certainty equivalent, and compute prices for defaultable bonds and dynamic protection against default. This latter price is interpreted as the premium for a contingent credit default swap, and connects our work with earlier articles, where the investor is protected upon default. We consider a multiple risky asset model with a single default time, at which point each of the assets may jump in price. Investment opportunities are driven by a diffusion X taking values in an arbitrary region . We allow for stochastic volatility, correlation, and recovery; unbounded random endowments; and postdefault trading. We identify the certainty equivalent with a semilinear parabolic partial differential equation with quadratic growth in both function and gradient. Under minimal integrability assumptions, we show that the certainty equivalent is a classical solution. Numerical examples highlight the relationship between the factor process, market dynamics, utility‐based prices, and default insurance premium. In particular, we show that the holder of a defaultable bond has a strong incentive to short the underlying stock, even for very low default intensities.     

The demand for risky assets under uncertain inflation : An examination of some widely used assumptions

This paper examines the effect of the following commonly used methods of incorporating random inflation into discrete-time models of the demand for risky assets: 1) the use of a multivariate normal probability distribution for nominal asset returns and the random inflation rate, and 2) the approximation of real asset returns by the difference between nominal returns and the rate of inflation. The combination of these assumptions results in a deceptively simple version of the inflationary capital asset pricing model (CAPM). However, in an approximation-free version of this model the expected value of real wealth does not exist. While it is obvious that mean-variance analysis is not applicable in such models, we also find that the model does not satisfy Ohlson's weakened conditions for a quadratic approximation to the portfolio selection problem. Furthermore, this model is neither a member of the generalized Pareto-Levy nor log-stable class of portfolio models analyzed by Fama, Samuelson, Ohlson, and Struck.     

Minimum variance cross hedging under mean‐reverting spreads,stochastic convenience yields,and jumps: Application to the airline industry

Exchange traded futures contracts often are not written on the specific asset that is a source of risk to a firm. The firm may attempt to manage this risk using futures contracts written on a related asset. This cross hedge exposes the firm to a new risk, the spread between the asset underlying the futures contract and the asset that the firm wants to hedge. Using the specific case of the airline industry as motivation, we derive the minimum variance cross hedge assuming a two‐factor diffusion model for the underlying asset and a stochastic, mean‐reverting spread. The result is a time‐varying hedge ratio that can be applied to any hedging horizon. We also consider the effect of jumps in the underlying asset. We use simulations and empirical tests of crude oil, jet fuel cross hedges to demonstrate the hedging effectiveness of the model. © 2009 Wiley Periodicals, Inc. Jrl Fut Mark 29:736–756, 2009     

Robust Hedging of Barrier Options

This article considers the pricing and hedging of barrier options in a market in which call options are liquidly traded and can be used as hedging instruments. This use of call options means that market preferences and beliefs about the future behavior of the underlying assets are in some sense incorporated into the hedge and do not need to be specified exogenously. Thus we are able to find prices for exotic derivatives which are independent of any model for the underlying asset. For example we do not need to assume that the underlying assets follow an exponential Brownian motion.
We find model-independent upper and lower bounds on the prices of knock-in and knock-out puts and calls. If the market prices the barrier options outside these limits then we give simple strategies for generating profits at zero risk. Examples illustrate that the bounds we give can be fairly tight.     

Disagreement in a Multi‐Asset Market

This paper provides a simple framework to study the effect of disagreement in a multi‐asset market equilibrium by considering two agents who disagree about expected returns, variances, and correlation of returns of two risky assets. When agents' subjective beliefs are characterized by mean preserving spreads of a benchmark homogeneous belief, we show that the effect of the disagreement does not cancel out in general and the effect in a multi‐asset market can be very different from a single asset market. In particular, the market risk premium can increase and the risk‐free rate can decrease significantly even when the market is overoptimistic and overconfident.     

DYNAMIC TRADING VOLUME

We derive the process followed by trading volume, in a market with finite depth and constant investment opportunities, where a large investor, with a long horizon and constant relative risk aversion, trades a safe and a risky asset. Trading volume approximately follows a Gaussian, mean‐reverting diffusion, and increases with depth, volatility, and risk aversion. Unlike the frictionless theory, finite depth excludes leverage and short sales because such positions may not be solvent even with continuous trading.     

上市公司终极控制权特征对定增标的资产估值的影响

标的资产“高溢价”导致上市公司业绩下滑、资产承诺业绩未达标事件激增,其中尤以定增并购标的资产与上市公司终极控制人关联交易最为突出。本文以我国沪深A股2007-2018年对终极控制人及其关联方实施过定向增发资产注入的上市公司为样本,分析终极控制权特征对标的资产估值的影响。结果表明:终极控制人的控制权与定增标的资产评估增值率呈“U”型关系,现金流权与定增标的资产的资产评估增值率负相关,两权分离度、控制权复杂度、定增前后终极控制人控制权的分离程度与定增标的资产评估增值率正相关;终极控制人在董事会占据席位的比例越大,经理人由终极控制人任命或担任的,定增标的资产评估增值率更高;民营性质的相较于国有性质的终极控制人,定增标的资产评估增值率更高,反映了机会主义行为动机下终极控制人的控制权地位显著影响定增标的资产估值,虚增的注入资产价值加剧了定增并购中的业绩承诺风险。终极控制人借助定增并购资产估值转移上市公司财富行为更具隐蔽性,投资者和监管部门需关注定增并购资产估值环节,有效预防业绩承诺风险。     

A NOTE ON THE EFFECTS OF TAXES ON OPTIMAL INVESTMENT

We integrate two approaches to portfolio management problems: that of Morton and Pliska (1995) for a portfolio with risky and riskless assets under transaction costs, and that of Cadenillas and Pliska (1999) for a portfolio with a risky asset under taxes and transaction costs. In particular, we show that the two surprising results of the latter paper, results shown for a taxable market consisting of only a single security, extend to a financial market with one risky asset and one bond: it can be optimal to realize not only losses but also gains, and sometimes the investor prefers a positive tax rate.     

THE SQUARED ORNSTEIN-UHLENBECK MARKET

We study a complete market containing J assets, each asset contributing to the production of a single commodity at a rate that is a solution to the squared Ornstein-Uhlenbeck (Cox-Ingersoll-Ross) SDE. The assets are owned by K agents with CRRA utility functions, who follow feasible consumption/investment regimes so as to maximize their expected time-additive utility from consumption. We compute the equilibrium for this economy and determine the state-price density process from market clearing. Reducing to a single (representative) agent, and exploiting the relation between the squared-OU and squared-Bessel SDEs, we obtain closed-form expressions for the values of bonds, assets, and options on the total asset value. Typical model parameters are estimated by fitting bond price data, and we use these parameters to price the assets and options numerically. Implications for the total asset price itself as a diffusion are discussed. We also estimate implied volatility surfaces for options and bond yields.