Pure jump models for pricing and hedging VIX derivatives

Recent non-parametric statistical analysis of high-frequency VIX data (Todorov and Tauchen, 2011) reveals that VIX dynamics is a pure jump semimartingale with infinite jump activity and infinite variation. To our best knowledge, existing models in the literature for pricing and hedging VIX derivatives do not have these features. This paper fills this gap by developing a novel class of parsimonious pure jump models with such features for VIX based on the additive time change technique proposed in Li et al., 2016a, Li et al., 2016b. We time change the 3/2 diffusion by a class of additive subordinators with infinite activity, yielding pure jump Markov semimartingales with infinite activity and infinite variation. These processes have time and state dependent jumps that are mean reverting and are able to capture stylized features of VIX. Our models take the initial term structure of VIX futures as input and are analytically tractable for pricing VIX futures and European options via eigenfunction expansions. Through calibration exercises, we show that our model is able to achieve excellent fit for the VIX implied volatility surface which typically exhibits very steep skews. Comparison to two other models in terms of calibration reveals that our model performs better both in-sample and out-of-sample. We explain the ability of our model to fit the volatility surface by evaluating the matching of moments implied from market VIX option prices. To hedge VIX options, we develop a dynamic strategy which minimizes instantaneous jump risk at each rebalancing time while controlling transaction cost. Its effectiveness is demonstrated through a simulation study on hedging Bermudan style VIX options.     

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.     

Cross‐hedging and forward‐contract pricing of electricity in the Pacific Northwest

This paper develops a linear regression model for using actively traded NYMEX natural gas futures as a cross‐hedge against electricity spot‐price risk in the Pacific Northwest and for pricing the forward contracts in the presence of temperature and hydro risks. Our approach comports with reality and provides power purchasers with an effective instrument through which they can hedge their electricity bets through natural gas futures. It also demonstrates the sharp month‐to‐month variations in the natural gas futures' optimal hedge ratios and hedge effectiveness. Finally, it finds significant risk premiums in the Pacific Northwest forward prices, supporting the hypothesis that forward‐contract buyers are relatively more risk‐averse than sellers. Copyright © 2011 John Wiley & Sons, Ltd.     

Model risk and option hedging

This paper presents a theoretical approach to option hedging and valuation when traders are facing model risk. Model risk is restrictively defined as the financial risk resulting from the choice of an approximating model to proxy for the true but ex-ante unknown state space of the underlying security process. A generalized model is defined for estimating the appropriate volatility markup, which is dependent on the noisiness of the volatility estimate over time. Delta neutral hedge portfolios are created using simulated S&P 500 option prices to demonstrate that using a volatility markup in the traditional binomial model reduces model risk.     

International tenders and futures hedging

This paper examines the optimal bidding and hedging decisions of a risk‐averse firm that takes part in an international tender. The firm faces multiple sources of uncertainty: exchange rate risk, risk of an unsuccessful tender, and business risk. The firm is allowed to trade unbiased currency futures contracts to imperfectly hedge its contingent foreign exchange risk exposure. We show that the firm shorts less (more) of the unbiased futures contracts when its marginal utility function is convex (concave) as compared with the case that the marginal utility function is linear. We further show that the curvature of the marginal utility function plays a decisive role in determining the impact of currency futures hedging on the firm's bidding behavior. Sufficient conditions that ensure the firm bids more or less aggressively than in the case without hedging opportunities are derived. Copyright © 2006 John Wiley & Sons, Ltd.     

Multi-step barrier products and static hedging

This paper examines multi-step barrier options with an arbitrary payoff function using extended static hedging methods. Although there have been studies using extended reflection principles to obtain joint distribution functions for barrier options with complex barrier conditions, and static hedging methods to evaluate limited barrier options with well-known payoff functions, we obtain an explicit expression of barrier option price which has a general payoff function under the Black–Scholes framework assumption. The explicit multi-step barrier options prices we discuss in this paper are not only useful in that they can handle different levels and time steps barrier and all types of payoff functions, but can also extend to pricing of barrier options under finite discrete jump–diffusion models with a simple barrier. In the last part, we supplement the theory with numerical examples of various multi-step barrier options under the Black–Scholes or discrete jump–diffusion model for comparison purposes.     

Managerial hedging ability and firm risk

Modern portfolio theory suggests that undiversified executives would choose to diversify their significant holdings of their firm??s stock if the opportunity was available. Recent work suggests that managerial hedging is more prevalent than in years past as more innovative hedging instruments have become available to executives. Typically, unrestricted shares are used in these hedging transactions whereas restricted shares are not. In this paper, I examine whether a CEO??s composition of firm stockholdings between restricted and unrestricted shares impacts the level of risk undertaken by the firm. I document a negative and statistically significant relationship between firm risk and the proportion of CEO total shareholdings that are unrestricted and this negative relationship holds for alternative measures of firm risk. This result supports the notion that the composition of a CEO??s portfolio of firm stock between restricted and unrestricted shares is a significant determinant of firm risk.     

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.     

Uncertain tax rules and futures hedging

This paper considers the optimal futures hedging decision under uncertain tax treatment. If the Corn Products (CP) rule applies, gains or losses from futures trading can offset business gains or losses. However, under the Arkansas Best (AB) doctrine, offsetting is not allowed. We show that the risk neutral firm will not trade futures contracts if the probability the CP rule prevails is small. When the probability is sufficiently large, the firm will assume an underhedge. A risk averse firm is likely to trade, even if the AB rule prevails. As long as the CP ruling is not a sure thing, the firm will engage in underhedge. The effects of average business profits, the volatility of business profits, and risk aversion on the optimal futures position are provided. Copyright © 1999 John Wiley & Sons, Ltd.     

Propensity for hedging and ambiguity aversion

We study ambiguity aversion by introducing some new notions of propensity for hedging that are less general than convexity of preferences. We therefore characterize the corresponding properties of the capacity and Choquet functional, and link them with actual observed behaviors under uncertainty (Fox et al., 1996; Tversky and Wakker, 1995).     

Corporate income tax and futures hedging

Our research is motivated by the Corn Products vs. Arkansas Best Supreme Court decisions that pitched the controversy of the tax treatment of gains and losses from futures hedging. The use of futures contracts as risk management tools depends on the tax code. In this paper we address complications in the current tax code that allow for asymmetric offset: Ordinary losses can be applied against capital gains; however, capital losses cannot by applied against ordinary gains. Also we consider the issue of tax loss carryover. We investigate the optimal hedge ratios under these scenarios analytically where possible, and numerically where necessary. Michael Metz is an independent commodity market consultant.     

债转股的博弈模型及政策探讨

在以债传股为主的银企债务重组中，政府-银行-资产管理公司-企业四者之间存在着既定的信息结构、契约关系和利益结构，本文通过建立银企债务重组的博弈模型，分析了肖前我国债转股中存在的若干问题及成因，进而提出相应的政策建议及措施。     

Local institutional shareholders and corporate hedging policies

This paper examines the effectiveness of monitoring function from institutional investors on corporate hedging strategy in Taiwan over the period from 2005 to 2012. The empirical results show that institutional investors are effective monitors of corporate risk management to enhance the probability and extent of hedging. In addition, the monitoring function from institutional investors is effective for mitigating the risk-shifting problem of high leveraged firms. Moreover, local institutional investors play more important role in monitoring distressed firm's magnitude of hedging than foreign institutional investors. These results are robust to the consideration of endogeneity, selection bias, and industrial difference. This is the first empirical evidence in the literature regarding the monitoring effect of institutional investors on risk management strategy from the angle of monitoring costs.     

互换价值的会计计量方法研究

互换作为一种新型的金融衍生工具,自上世纪八十年代以来,在风险管理中得到广泛的应用。互换所产生的价值具有十分重要的意义,而这种价值在会计中应选用何种方法加以计量,成为会计界与金融界特别关注的问题。本文针对两种涵义提出两种计量方法,并分别对其特点进行分析,从中选出一种更加合理的方法,为互换价值的会计计量提供借鉴。     

Tax‐loss carryforward and futures hedging

Our research is motivated by the Corn Products vs Arkansas Best Supreme court decisions that brought on the controversy of the tax treatment of gains and losses from futures hedging. The usefulness of a futures contract as risk management tool depends on the tax code. In this paper we address implications of capital treatment of futures positions (disallowing offset for tax purposes) when tax‐loss carryover is allowed. Our analysis utilizes a two‐period model to capture the inter‐temporal effects. We investigate the optimal hedge ratios under these scenarios analytically where possible, and numerically where necessary. Copyright © 2002 John Wiley & Sons, Ltd.     

Immunizing Foreign Exchange Contracts Against Swap Rate and Volatility Risks

Swap rate risk, also called the problem of' "maturity gaps," originates from foreign currency holdings whenever the involved contracts have differing maturities. Such differing maturities give rise to a sensitivity of the portfolio values with respect to the "swap rate," or differential between the relative interest rates in two countries. Volatility risk, which typically affects only currency contracts having asymmetric payoffs (such as currency options), gives rise to a sensitivity of portfolio values with respect to changes in the exchange rate volatility. In this article we show how currency portfolios may be immunized , or made insensitive, to both swap rate risk and volatility risk, in the sense of Macaulay's (1938) classical treatment of interest rate risk. The European currency option contract is the primary subject of our discussion, since we show that both ordinary forward contracts and other complicated currency contracts are equivalent to suitable combinations of European currency options.     

Tax asymmetry and futures hedging under liquidity constraints

This paper examines the optimal futures hedging decision of a firm facing uncertain income that is subject to asymmetric taxation with no loss‐offset provisions. All futures contracts are marked to market and require interim cash settlement of gains and losses. The firm is liquidity constrained in that it is forced to prematurely close its futures position on which the interim loss incurred exceeds a threshold level. The liquidity risk created by the interim funding requirement of a futures hedge is shown to proffer the firm perverse incentives, thereby making an under‐hedge optimal. This under‐hedging result holds irrespective of whether the firm is risk neutral or risk averse. Copyright © 2005 John Wiley & Sons, Ltd.     

International trade and hedging in economies in transition

This paper develops a general equilibrium framework to analyze risk management policies in economies in transition. By cross-hedging against real exchange rate risk exposures, these economies can increase their gains from international trade. We suggest that countries with emerging forward markets can gradually introduce the risk sharing markets, as limiting resources may prevent them from introducing complete hedging markets in the first place. Thus the growing demand for risk management instruments can be gradually met and it would be welfare enhancing. Economies in transition benefit when hedging devices are offered by financial markets, irrespective of whether the hedging instruments are de facto perfect or not.     

Production and hedging under correlated price and background risks

Decisions in Economics and Finance - This paper examines the competitive firm that has to make its production and hedging decisions under correlated price and background risks. The background risk...