Perfect hedging under endogenous permanent market impacts

We model a nonlinear price curve quoted in a market as the utility indifference curve of a representative liquidity supplier. As the utility function, we adopt a \(g\)-expectation. In contrast to the standard framework of financial engineering, a trader is no longer a price taker as any trade has a permanent market impact via an effect on the supplier’s inventory. The P&L of a trading strategy is written as a nonlinear stochastic integral. Under this market impact model, we introduce a completeness condition under which any derivative can be perfectly replicated by a dynamic trading strategy. In the special case of a Markovian setting, the corresponding pricing and hedging can be done by solving a semilinear PDE.     

价格异常与不对称相关结构下套期保值策略——来自亚洲股指期货市场的实证

在不对称相关结构下,尾部区域期货和现货价格联动模式异常复杂,传统套期保值策略在极端价格行为下将不可避免地出现系统性偏差。为此,恰当的连接函数被引入描述尾部区域的价格联动模式,依据MV框架构建局部套期保值策略,以解决极端价格行为下的套期保值问题。对亚洲市场日经指数和恒生指数期货套期保值的实证研究表明:(1)采用Rotated Gumbel连接函数,在传统MV策略(全局策略)下,虽然在降低套保组合方差方面没有明显优势,但日经指数和恒生指数期货的套期保值成本将显著下降,套保组合收益/组合方差的比率显著上升;(2)如果套期保值者能够对未来形成可靠预期,套期保值的成本将进一步下降,并且现货价格风险也得到有效控制。     

Minimum variance hedging when spot price changes are partially predictable

In many markets, changes in the spot price are partially predictable. We show that when this is the case: (1) although unbiased, traditional regression estimates of the minimum variance hedge ratio are inefficient, (2) estimates of the riskiness of both hedged and unhedged positions are biased upward, and (3) estimates of the percentage risk reduction achievable through hedging are biased downward. For natural gas cross hedges, we find that both the inefficiency and bias are substantial. We further find that incorporating the expected change in the spot price, as measured by the futures-spot price spread at the beginning of the hedge, into the regression results in a substantial increase in efficiency and reduction in the bias.     

The price of a smile: hedging and spanning in option markets

The volatility smile changed drastically around the crash of1987, and new option pricing models have been proposed to accommodatethat change. Deterministic volatility models allow for moreflexible volatility surfaces but refrain from introducing additionalrisk factors. Thus, options are still redundant securities.Alternatively, stochastic models introduce additional risk factors,and options are then needed for spanning of the pricing kernel.We develop a statistical test based on this difference in spanning.Using daily S&P 500 index options data from 1986-1995, ourtests suggest that both in- and out-of-the-money options areneeded for spanning. The findings are inconsistent with deterministicvolatility models but are consistent with stochastic modelsthat incorporate additional priced risk factors, such as stochasticvolatility, interest rates, or jumps.     

Optimal and equilibrium execution strategies with generalized price impact

This paper examines the execution problems of large traders with a generalized price impact. Constructing two related models in a discrete-time setting, we solve these problems by applying the backward induction method of dynamic programming. In the first problem, we formulate the expected utility maximization problem of a single large trader as a Markov decision process and derive an optimal execution strategy. Then, in the second model, we formulate the expected utility maximization problem of two large traders as a Markov game and derive an equilibrium execution strategy at a Markov perfect equilibrium. Both of these two models enable us to investigate how the execution strategies and trade performances of a large trader are affected by the existence of other traders. Moreover, we find that these optimal and equilibrium execution strategies become deterministic when the total execution volumes of non-large traders are deterministic. We also show, by some numerical examples, the comparative statics results with respect to several problem parameters.     

The impact of nominal stock price on ex-dividend price responses

In this paper, we examine whether nominal stock price can help to explain the ex-dividend day anomaly where stock prices drop by less than the dividend amount on the ex-dividend date. We find that stocks with lower nominal prices have ex-dividend day price drops that are more consistent with theoretical predictions based on an efficient market. After controlling for factors that have been previously documented to influence ex-dividend day stock price behavior, price-drop-to-dividend ratios are closer to one for lower priced stocks. To further explore this phenomenon, we examine the change in the price-drop-to-dividend ratio around stock splits. Firms that split their shares have a larger price-drop-to-dividend ratio after the split, and companies that reverse split their shares have a smaller price-drop-to-dividend ratio after the split. Our evidence indicates that ex-dividend day stock price behavior is influenced by the nominal price of a share and that this relation could also influence the decision to split a firm’s shares.     

Fiscal hedging with nominal assets

We analyze optimal fiscal and monetary policy in an economy with distortionary labor income taxes, nominal rigidities, nominal debt of various maturities and short-selling constraints. Optimal policy prescribes the almost exclusive use of long term debt. Such debt mitigates the distortions associated with hedging fiscal shocks by allowing the government to allocate them efficiently across states and periods.     

Financial hedging with derivatives and its impact on the Colombian market value for listed companies

The financial theory (Modigliani & Miller, 1958) presents risk management as a matter without importance in companies, given that the shareholders themselves managed their hedges, diversifying their portfolios. However, subsequent studies dispute said premise and present evidence that business financial hedging improves performance and increases the value of the same (Ahmed, Azevedo, & Guney, 2014; Allayannis & Weston, 2001; Kapitsinas, 2008). The efficient market risk management is supported in the financial derivatives, and demands strategic and efficient administrators in hedges that add value, especially in the face of clashes and macroeconomic and financial imbalances. The empirical evidence analyzes the behavior of the Q-Tobin as an indicator of the effect of the hedge strategies for the exchange rate associated to the market value. The aim of this work is to find evidence in Colombia on the effect of the use of derivatives in the market value of the company. Its added value lies in the analysis that is done by economic sectors, identified by ISIC codes and grouped into five (5) macro sectors (Agriculture and livestock, Commercial, Industrial or Manufacture, Services, and Construction). The methodology used includes the estimation of several regression models in data panels, using a Pooled regression model with fixed and random effect estimators through the maximum likelihood estimator. In general, a statistical and financially significant premium for hedges was found for companies exposed to exchange rate risks that use derivatives of a 6.3% average on the market value. Additionally, mixed results were found in relation to the variables analyzed in the model.     

Order book approach to price impact

Buying and selling stocks causes price changes, which are described by the price impact function. To explain the shape of this function, we study the Island ECN orderbook. In addition to transaction data, the orderbook contains information about potential supply and demand for a stock. The virtual price impact calculated from this information is four times stronger than the actual one and explains it only partially. However, we find a strong anticorrelation between price changes and order flow, which strongly reduces the virtual price impact and provides for an explanation of the empirical price impact function.     

Adapted hedging

Exponentials of squared returns in Gaussian densities, with their consequently thin tails, are replaced by the absolute return to form Laplacian and exponentially tilted Laplacian densities at unit time. Scaling provides densities at other maturities. Stochastic processes with these marginals are identified. In addition to a specific local volatility model the densities are consistent with the difference of compound exponential processes taken at log time and scaled by the square root of time. The underlying process has a single parameter, the constant variance rate of the process. Delta hedging using Laplacian and Asymmetric Laplacian implied volatilities are developed and compared with Black Merton Scholes implied volatility hedging.The hedging strategies are implemented for stylized businesses represented by dynamic volatility indexes. The Laplacian hedge is seen to be smoother for the skew trade. It also performs better through the financial crisis for the sale of strangles. The Laplacian and Gaussian models are then synthesized as special cases of a model allowing for other powers between unity and the square. Numerous hedging strategies may be run using different powers and biases in the probability of an up move. Adapted strategies that select the best performer on past quarterly data can dominate fixed strategies. Adapted hedging strategies can effectively reduce drawdowns in the marked to market value of businesses trading options.     

A functional approach to the price impact of stock trades and the implied true price

We propose a functional approach to estimate the instantaneous price impact of a trade and to infer an implied true price. Our model expresses price impact as an S-shaped function of signed volume. It has two parameters, one for price impact and one for liquidity depth. The latter measures the differential impact of small and large trades. The price impact is instantaneous, that is, it occurs at the instant of trade execution. Our specification also permits the price impact of buys and sells to be asymmetric. We compute an implied true price from our model, and we find that it is closer than the quote midpoint to the unobservable true price. Our empirical analysis also shows that the effective spread, which is computed using the midpoint, has an upward bias, and that the implicit transaction costs may be lower than previous estimates.     

New evidence on price impact of analyst forecast revisions

Previous research shows a positive relationship between consensus forecast revisions and stock returns in developed markets. We obtain new evidence from four major Asia-Pacific markets that suggest that abnormal returns are related to latest forecast revisions. The price impact of negative revisions is consistently stronger than that of the positive revisions. We also found considerable differences in price impact between developed and emerging markets for positive revisions, while no such difference is detected for negative revisions. The latest forecast revisions and category of analysts (those working in international broking firms) appear to be two key determinants of abnormal stock returns.     

Measuring the impact of sales on earnings and equity price

In this paper we examine how sales affect earnings and in turn the stock price using a model in which sales contribute to earnings by a fixed sales margin rate and the stock price responds more sensitively to sales-induced earnings than to non-sales-induced earnings. We report that the regression coefficient of the sales margin (2.54) is about three times the earnings response coefficient (0.85) for the full sample and can be as high as 19 times the earnings response coefficient for an industry (i.e., 11.95 vs. 0.62 for restaurants). We contribute to the literature by identifying and documenting factors that make separating out the sources of earnings more important in equity pricing.

Regime switching correlation hedging

This paper investigates the hedging effectiveness of commodity futures when the correlations of spot and futures returns are subject to multi-state regime shifts. An independent switching dynamic conditional correlation GARCH (IS-DCC) which is free from the problems of path-dependency and recombining is applied to model multi-regime switching correlations. The results of hedging exercises indicate that state-dependent IS-DCC outperforms state-independent DCC GARCH and three-state IS-DCC exhibits superior hedging effectiveness, illustrating importance of modeling higher-state switching correlations for dynamic futures hedging.     

Optimal static quadratic hedging

We propose a flexible framework for hedging a contingent claim by holding static positions in vanilla European calls, puts, bonds and forwards. A model-free expression is derived for the optimal static hedging strategy that minimizes the expected squared hedging error subject to a cost constraint. The optimal hedge involves computing a number of expectations that reflect the dependence among the contingent claim and the hedging assets. We provide a general method for approximating these expectations analytically in a general Markov diffusion market. To illustrate the versatility of our approach, we present several numerical examples, including hedging path-dependent options and options written on a correlated asset.     

Dynamic programming and mean-variance hedging with partial execution risk

In this paper I consider a hedging problem in an illiquid market where there is a risk that the hedger’s order to buy or sell the underlying asset may be executed only partially. In this setting, I find a mean-variance optimal hedging strategy by the dynamic programming method. The solution contains a new endogenous state variable representing the current position in the underlying. The exogenous coefficients in the solution are given by recursive formulas which can be calculated efficiently in Markov models. I illustrate effects of the partial execution risk in several examples.      

A generalized approach to optimal hedging with option contracts

In this paper, we develop a theoretical model in which a firm hedges a spot position using options in the presence of both quantity (production) and basis risks. Our optimal hedge ratio is fairly general, in that the dependence structure is modeled through a copula function representing the quantiles of the hedged position, and hence any quantile risk measure can be employed. We study the sensitivity of the exercise price which minimizes the risk of the hedged portfolio to the relevant parameters, and we find that the subjective risk aversion of the firm does not play any role. The only trade-off is between the effectiveness and cost of the hedging strategy.