Arbitrage-free Interval Research Articles

A cooperative governance model for SO2 emission rights futures that accounts for GDP and pollutant removal cost

Due to the cross-regional mobility of air pollution, the traditional governance mode has been difficult to implement effectively. To solve the problem of excessive pollution governance costs, we determined the spot price of emission futures with a pricing model based on an arbitrage-free interval, and constructed a dual-objective optimization model that accounts for both GDP and the pollutant removal cost. By comparing the optimal removal volumes for each cooperator with the national allocation of removal quotas, we divided actors into sellers and buyers of cooperative emission rights based on futures trading. Finally, we used an asymmetric Nash negotiation model to distribute the benefits of cooperation. To demonstrate the approach, we used China’s Beijing-Tianjin-Hebei region as a case study, and found that the cooperative governance strategy can help to solve the air pollution problem. Compared with the independent autonomy model of the futures market, the Cooperative Governance Model (CGM) increased the GDP of the Beijing-Tianjin-Hebei region by 22.143 × 109 Yuan, an increase of 0.3 %, and decreased the removal cost by 124.030 × 106 Yuan, a decrease of 0.4 %. Our results provide a reference for policy decisions on collaborative air pollution control, and can be used to promote collaborative air pollution control in other regions.

AN INTERVAL OF NO-ARBITRAGE PRICES FOR AMERICAN CONTINGENT CLAIMS IN INCOMPLETE MARKETS

In this paper we establish an arbitrage-free prices interval for American contingent claims in incomplete financial markets. Such an incom- pleteness derives from considering uncertain volatility. We use the notion of G-expectation, under which the corresponding canonical path is a G-Brownian Motion, and the related Ito stochastic calculus on suitable stopping time inter- vals, in a standard financial market characterized by a risk-less asset and one risky stock.

Empirical analysis on future-cash arbitrage risk with portfolio VaR

This paper constructs the positive arbitrage position by alternating the spot index with Chinese Exchange Traded Fund (ETF) portfolio and estimating the arbitrage-free interval of futures with the latest trade data. Then, an improved Delta-normal method was used, which replaces the simple linear correlation coefficient with tail dependence correlation coefficient, to measure VaR (Value-at-risk) of the arbitrage position. Analysis of VaR implies that the risk of future-cash arbitrage is less than that of investing completely in either futures or spot market. Then according to the compositional VaR and the marginal VaR, we should increase the futures position and decrease the spot position appropriately to minimize the VaR, which can minimize risk subject to certain revenues.

Calibrated American option pricing by stochastic linear programming

We propose an approach for computing the arbitrage-free interval for the price of an American option in discrete incomplete market models via linear programming. The main idea is built replicating strategies that use both the basic asset and some European derivatives available on the market for trading. This method goes under the name of calibrated option pricing and it has given significant results for European options. Here, we extend the analysis to American options showing that the arbitrage-free interval can be characterized in terms of martingale measures and that it gets significantly reduced with respect to the non-calibrated case.

Option pricing by mean correcting method for non-Gaussian Lévy processes

For a non-Gaussian Levy model, it is shown that if the model exists a trivial arbitrage-free interval, option pricing by mean correcting method is always arbitrage-free, and if the arbitrage-free interval is non-trivial, this pricing method may lead to arbitrage in some cases. In the latter case, some necessary and sufficient conditions under which option price is arbitrage-free are obtained.

Utility maximization in markets with bid–ask spreads

A one-period financial market model with transaction costs is considered in this paper. Redefining the risky asset price process in a suitable way, we obtain an explicit solution to the utility maximization problem when the risk preferences of the investor are based on the exponential utility function and a liability can be included in her portfolio. The arbitrage-free interval price for a general liability, as well as its replication price, is characterized in terms of expectations with respect to equivalent martingale measures. The indifference price is derived and its asymptotic limit when the risk aversion is going to infinity is analysed.

No arbitrage pricing of non-marketed claims in multi-period markets

In this paper, we modify the arbitrage-free interval of prices for a non-marketed contingent claim in the finite event-tree model of financial markets, according to the perfect hedging approach being well-known for the two-period model. We prove the existence of solution to the corresponding seller's and buyer's price problem for such a claim under no-arbitrage prices for the marketed contracts and we show that each of these problems can be solved by decomposing it into a finite number of one-period linear programming problems solved backwards. Finally, we indicate that the set of the no-arbitrage prices for a non-marketed contingent claim is the interval of the real numbers whose supremum and infimum is the seller's and the buyer's price of the claim, respectively. The determination of the set of no-arbitrage prices for a non-marketed contingent claim is related to the utility pricing of such a claim.

Arbitrage-Free Interval and Dynamic Hedging in an Illiquid Market

This paper provides two modified pricing PDEs for a general European option under liquidity risk, by which two modified hedges are derived. It is shown that the hedge errors of the two modified hedges approach zero as the trading time interval converges to zero inclusive of liquidity costs. An arbitrage-free interval is identified and in contrast to transaction costs, the liquidity cost is proved to be finite even if trading is continuous. Numerical results are presented on option pricing and the moments of hedge errors with both Black-Scholes hedge and one of the modified hedge. The results indicate that under liquidity risk, the modified option hedge developed in this paper is much superior to the Black-Scholes hedge. The bigger the liquidity risk, the more significant the advantages. In fact, the modified hedge leads to not only a much less hedge error but also to a lower replication costs than the classical Black-Scholes hedge.

Arbitrage-free interval and dynamic hedging in an illiquid market

This paper derives two pricing PDEs for a general European option under liquidity risk. We provide two modified hedges: one hedge replicates a short option and the other replicates a long option inclusive of liquidity costs under continuous rebalancing. We identify an arbitrage-free interval by calculating the costs of the two hedges. Unlike in a setting with infinite overall transaction costs, the overall liquidity cost in our model is proved to be finite even under continuous rebalancing. Numerical results on option pricing and the moments of hedge errors of Black–Scholes and our modified hedges are also presented.

Arbitrage-free interval of American contingent claims under proportional transaction cost

In a general continuous-time market model with proportional transaction costs, we derive the range of arbitrage-free prices of American contingent claims. Using a martingale approach, we obtain the upper and the lower hedging price of American contingent claims.

On the pricing of American contingent claims under transaction costs and multiple risky assets

Abstract This paper addresses the hedging problem of American Contingents Claims (ACCs) in the framework of continuous-time Ito models for financial market. The special feature of this paper is that in the financial market the investor has to face fixed and proportional transaction costs when trading multiple risky assets. By using the auxiliary martingale approach and extending the results of Cvitanic and Karatzas [Cvitanic J, Karatzas I. Hedging and portfolio optimization under transaction costs: a martingale approach. Math Finance 1996;6:135–65] on pricing European contingent with transaction costs in the single-stock market, an arbitrage-free interval [hlow, hup] is identified, and the end points are characterized by auxiliary martingales and stopping times in terms of auxiliary stochastic control problems. Here hup and hlow are so-called the upper hedging price and the lower hedging price.

Hedging American contingent claims with constrained portfolios under proportional transaction costs

In a general continuous-time market model with constrained portfolios under proportional transaction costs, we derive the upper and lower hedging prices of American contingent claims. Furthermore we have that [ h low ( K ), h up ( K )] is an arbitrage-free interval.

On the Pricing of Contingent Claims with Frictions

This paper studies the problem of pricing contingent claims in a market which has frictions in the form of costs, such as penalty functions corresponding to constraints. An arbitrage-free interval is identified, and a fair price based upon utility functions is proposed. It provides a framework to study incomplete markets that is simplier than the one related to constraints on portfolios introduced by Karatzas and Kou.

On the pricing of contingent claims under constraints

We discuss the problem of pricing contingent claims, such as European call options, based on the fundamental principle of absence of arbitrage and in the presence of constraints on portfolio choice, for example, incomplete markets and markets with short-selling constraints. Under such constraints, we show that there exists an arbitrage-free interval which contains the celebrated Black-Scholes price (corresponding to the unconstrained case); no price in the interior of this interval permits arbitrage, but every price outside the interval does. In the case of convex constraints, the endpoints of this interval are characterized in terms of auxiliary stochastic control problems, in the manner of Cvitanic and Karatzas. These characterizations lead to explicit computations, or bounds, in several interesting cases. Furthermore, a unique fair price $\hat{p}$ is selected inside this interval, based on utility maximization and marginal rate of substitution principles. Again, characterizations are provided for $\hat{p}$, and these lead to very explicit computations. All these results are also extended to treat the problem of pricing contingent claims in the presence of a higher interest rate for borrowing. In the special case of a European call option in a market with constant coefficients, the endpoints of the arbitrage-free interval are the Black-Scholes prices corresponding to the two different interest rates, and the fair price coincides with that of Barron and Jensen.