The Minimal Entropy Martingale Measures for Exponential Additive Processes

In this paper, we will consider exponential additive processes as a financial market model. Under a mild condition, we will determine the minimal entropy martingale measures (MEMMs) for the exponential additive processes. To this end, we will prepare several results on the exponential moment of additive processes and integrals based on them. As an application of our result, we will deduce optimal strategy for exponential utility maximization problem. We will also investigate our result through several examples, such as time-dependent versions of double Poisson model, Merton model and Kou model.     

Hedging with Chinese metal futures

This paper evaluates different hedging strategies for aluminum and copper futures contracts traded at Shanghai Futures Exchange. In addition to usual candidates such as the traditional regression hedge ratio and the hedging strategy constructed from bivariate fractionally integrated generalized autoregressive conditional heteroskedasticity (BFIGARCH) model, two advanced specifications are proposed to account for impacts of the basis on market volatility and co-movements between spot and futures returns. Empirical results suggest that the basis has asymmetric effects and optimal hedging strategy constructed from the asymmetric BFIGARCH model tends to produce the best in-sample and out-of-sample hedging performance.     

Hedging with small uncertainty aversion

We study the pricing and hedging of derivative securities with uncertainty about the volatility of the underlying asset. Rather than taking all models from a prespecified class equally seriously, we penalise less plausible ones based on their “distance” to a reference local volatility model. In the limit for small uncertainty aversion, this leads to explicit formulas for prices and hedging strategies in terms of the security’s cash gamma.     

On Discrete-Time Dynamic Programming in Insurance: Exponential Utility and Minimizing the Ruin Probability

This paper studies an insurance model where the risk process can be controlled by reinsurance and by investment in a financial market. The performance criterion is either the expected exponential utility of the terminal surplus or the ruin probability. It is shown that the problems can be imbedded in the framework of discrete-time stochastic dynamic programming but with some special features. A short introduction to control theory with infinite state space is provided which avoids the measure-theoretic apparatus by use of the so-called structure assumption. Moreover, in order to treat models without discount factor, a weak contraction property is derived. Explicit conditions are obtained for the optimality of employing no reinsurance.     

Hedging long-term exposures with multiple short-term futures contracts

This article analyzes the problem facing an agent who has along-term commodity supply commitment and who wishes to hedgethat commitment using short-maturity commodity futures contracts.As time evolves, the agent has to roll the hedge as old futurescontracts mature and new futures contracts are listed. Thisgives rise to hedge errors. The optimal hedging strategy ischaracterized in a world where contracts of several differentmaturities coexist. The strategy is independent both of theagent's risk aversion and, under certain conditions, of beliefsabout expected returns from holding futures contracts. The methodologyis compared with approaches based on dynamic models of the termstructure. It is tested on data from the oil futures market.     

An International Asset Pricing Model with Time-Varying Hedging Risk

This paper employs a two-factor international equilibrium asset pricing model to examine the pricing relationships among the world's five largest equity markets. In addition to the traditional market factor premium, a hedging factor premium is included as the second factor to explain the relationship between risks and returns in the international stock markets. Moreover, a GARCH parameterization is adopted to characterize the general dynamics of the conditional second moments. The results suggest that the additional hedging risk premium is needed to explain rates of return on international equities. Furthermore, the restriction that the coefficient on the hedge-portfolio covariance is one smaller than the coefficient on the market-portfolio covariance can not be rejected. This suggests that the intertemporal asset pricing model proposed by Campbell (1993) can be used to explain the returns on the five largest stock market indices.     

Optimal Hedging in Futures Markets with Multiple Delivery Specifications

Nearly all futures contracts allow delivery of any of several qualities of the underlying asset. Consequently, the price of the futures contract is associated more with the price of the expected cheapest deliverable variety than with the price of the par-delivery variety. The delivery specifications introduce a delivery risk for every hedger in the market. We derive the optimal hedging strategies in these markets. Their hedging effectiveness is evaluated for wheat futures contracts in Chicago. Hedging optimally would have significantly reduced the variance of the rates of return on hedges while yielding similar mean returns.     

Hedging Long-Term Forwards with Short-Term Futures: A Two-Regime Approach

In this paper we investigate Metallgesellschafts problem of hedging long-term forwards with short-term futures. Very different hedging strategies have been proposed in the literature. We attribute these differences to the underlying valuation approaches for oil futures and empirically compare five model-based hedging strategies. In particular, we consider a strategy which results from a two-regime pricing model. This continuous-time equilibrium model reflects the observation that prices of oil futures exhibit a very different behavior for low and high oil prices. Our empirical study shows that time diversification is the dominant effect for an effective hedging of long-term oil forwards with short-term futures. JEL classification G13, G30     

Exponential moments for HJM models with jumps

General HJM models driven by a Lévy process are considered. Necessary moment conditions for the discounted bond prices to be local martingales are derived. Under these moment conditions, it is proved that the discounted bond prices are local martingales if and only if a generalized HJM condition holds. Research supported in part by Polish KBN Grant P03A 034 29 “Stochastic evolution equations driven by Lévy noise”.     

Properties of Multinomial Lattices with Cumulants for Option Pricing and Hedging

In this paper, we analyze properties of multinomial lattices that model general stochastic dynamics of the underlying stock by taking into account any given cumulants (or moments). First, we provide a parameterization of multinomial lattices, and demonstrate that mean, variance, skewness, and kurtosis of the underlying may be matched using five branches. Then, we investigate the convergence of the multinomial lattice when the basic time period approaches zero, and prove that the limiting process of the multinomial lattice that matches annualized mean, variance, skewness and kurtosis is given by a compound Poisson process. Finally, we illustrate the effect of higher order moments in the underlying asset process on the price of derivative securities through numerical experiments using the multinomial lattice, and provide a comparison with jump-diffusion models.     

Portfolio Selection with Quadratic Utility Revisited

Considering a simple portfolio selection problem by agents with quadratic utility, an apparently counterintuitive outcome results. When such a choice is over two assets that can be ordered in terms of riskiness, an agent that is more risk averse may optimally invest a larger portion of wealth in the riskier asset. It is shown that such an outcome is not counterintuitive, since for the portfolios from which agents optimally choose, a larger proportion of investment in the riskier asset leads to a less risky portfolio.     

Hedging errors with Leland's option model in the presence of transaction costs

Nonzero transaction costs invalidate the Black–Scholes [1973. Journal of Political Economy 81, 637–654] arbitrage argument based on continuous trading. Leland [1985. Journal of Finance 40, 1283–1301] developed a hedging strategy which modifies the Black–Scholes hedging strategy with a volatility adjusted by the length of the rebalance interval and the rate of the proportional transaction cost. Kabanov and Safarian [1997. Finance and Stochastics 1, 239–250] calculated the limiting hedging error of the Leland strategy and pointed out that it is nonzero for the approximate pricing of an European call option, in contradiction to Leland's claim. As a further contribution, we first identify the mathematical flaw in the argument of Leland's claim and then quantify the expected percentage of hedging losses in terms of the hedging frequency and the level of the option strike price.     

Hedging Strategies of Financial Intermediaries: Pricing Options with a Bid-Ask Spread

This paper uses a model similar to the Boyle-Vorst and Ritchken-Kuo arbitrage-free models for the valuation of options with transactions costs to determine the maximum price to be charged by the financial intermediary writing an option in a non-auction market. Earlier models are extended by recognizing that, in the presence of transactions costs, the price-taking intermediary devising a hedging portfolio faces a tradeoff: to choose a short trading interval with small hedging errors and high transactions costs, or a long trading interval with large hedging errors and low transactions costs. The model presented here also recognizes that when transactions costs induce less frequent portfolio adjustments, investors are faced with a multinomial distribution of asset returns rather than a binomial one. The price upper bound is determined by selecting the trading frequency that will equalize the marginal gain from decreasing hedging errors and the marginal cost of transactions.     

Corporate Bond Valuation and Hedging with Stochastic Interest Rates and Endogenous Bankruptcy

This paper analyzes corporate bond valuation and optimal calland default rules when interest rates and firm value are stochastic.It then uses the results to explain the dynamics of hedging.Bankruptcy rules are important determinants of corporate bondsensitivity to interest rates and firm value. Although endogenousand exogenous bankruptcy models can be calibrated to producethe same prices, they can have very different hedging implications.We show that empirical results on the relation between corporatespreads and Treasury rates provide evidence on duration, andwe find that the endogenous model explains the empirical patternsbetter than do typical exogenous models.     

Option Valuation and Hedging Strategies with Jumps in the Volatility of Asset Returns

We develop a model in which the volatility of risky assets is subject to random and discontinuous shifts over time. We derive prices of claims contingent on such assets and analyze options-based trading strategies to hedge against the risk of jumps in the return volatility. Unsystematic and systematic events such as takeovers, major changes in business plans, or shifts in economic policy regimes may drastically alter firms' risk profiles. Our model captures the effect of such events on options markets.     

Option Pricing with Threshold Diffusion Processes

The threshold diffusion (TD) model assumes a piecewise linear drift term and piecewise smooth diffusion term, which can capture many nonlinear features and volatility clustering often observed in financial time series data. We solve the problem of option pricing with a TD asset pricing process by deriving the minimum entropy martingale measure, which is the risk-neutral measure closest to the underlying TD probability measure in terms of Kullback-Leibler divergence, given the historical regime-switching pattern. The proposed valuation model is illustrated with a numerical example.     

Hedging with Chinese Aluminum Futures: International Evidence with Return and Volatility Spillover Indices Under Structural Breaks

This paper examines the hedging performance of the Shanghai futures market, with the London futures market acting as the channel for volatility spillover. Taking into consideration structural change, basis effects, and return and volatility spillover effects, the authors find that the estimated hedging performance is not improved. Their findings suggest that the effectiveness of the hedging performance of aluminum futures contracts in China is not affected by the magnitude or direction of return and volatility spillovers. Therefore, even when the magnitude and direction of volatility spillover from other markets can be correctly predicted, the hedging performance of a futures contract cannot be significantly improved. This paper uses precise measures of return spillovers and volatility spillovers based directly on the framework of vector autoregressive variance decompositions. The study also includes an analysis of both crisis and noncrisis episodes, with modeling on bursts in spillovers.     

A Note on Utility Maximization with Unbounded Random Endowment

This paper addresses the applicability of the convex duality method for utility maximization, in the presence of random endowment. When the underlying price process is a locally bounded semimartingale, we show that the fundamental duality relation holds true, for a wide class of utility functions and unbounded random endowments. We show this duality by exploiting Rockafellar’s theorem on integral functionals, to a random utility function.