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This paper discusses finding solutions to the modified Fractional Black–Scholes equation. As is well known, the options theory is beneficial in the stock market. Using call-and-pull options, investors can theoretically decide when to sell, hold, or buy shares for maximum profits. However, the process of forming the Black–Scholes model uses a normal distribution, where, in reality, the call option formula obtained is less realistic in the stock market. Therefore, it is necessary to modify the model to make the option values obtained more realistic. In this paper, the method used to determine the solution to the modified Fractional Black–Scholes equation is a combination of the finite difference method and the fractional differential transformation method. The results show that the combined method of finite difference and fractional differential transformation is a very good approximation for the solution of the Fractional Black–Scholes equation. [ABSTRACT FROM AUTHOR]

In this article, we analyse the impact of the introduction of options on an investment portfolio. Our first objective is to derive closed-form formulae for the standard measures of portfolio efficiency: risk premium, risk, Sharpe ratio, and beta, of any portfolio containing any combination of options. Using these formulae on three examples of simple option strategies (call overwriting, put protection, and collars), we show how these statistics are altered by the inclusion of an option overlay in a portfolio. Our second objective is to show that if an option strategy is repeated over multiple investment time periods, the long-run return becomes normally distributed. Our motivation is to provide investors with the mathematics to measure the impact of the introduction of options on portfolio efficiency and encourage a potential portfolio rebalance to account for this impact. Then, we highlight that whilst options can create asymmetric non-normal outcomes, their repeated use may not alter the long-run portfolio return in the desired way and thus to encourage investors to assess if an option overlay will deliver the desired long-run outcome. [ABSTRACT FROM AUTHOR]

The article discusses impact of failure of African Bank on the markets and financial system of South Africa and mentions use of Merton structural model to evaluate the bank's financial health. It discusses several factors that serve as the basis for assessment including capital protection, asset quality management and liquidity. It also discusses role of market prices of a company's securities in terms of debt and equity.

To study risk coordination of supply chains, a two-echelon supply chain with one risk-neutral supplier and one risk-averse retailer is constructed, in which the retailer behaves with waste aversion. The retailer's conservative attitude to order results in poor performance of the supplier and the whole supply chain. A new contract which combines put options and selective return policies is developed. The retailer buys option contracts when he places an order, then decides to exercise part or all of them after the sales season so that he can choose the return quantity selectively. The exercise price is equivalent to the wholesale price of merchandise. The result demonstrates that this contract can coordinate the supply chain well and be carried out normally despite the retailer's risk preference being private because the supplier's pricing policy is independent of retailer's risk aversion. The numerical analysis shows that the retailer's expected utility outperforms that of the expected utility under the classical buyback contract. [ABSTRACT FROM AUTHOR]

The port logistics finance has been developed rapidly under the port low-carbon transition development. It was very urgent for research on port logistics pledge loan portfolio optimization decision-making theory under the low-carbon transition. In this study, the port pledge loan under the low-carbon transition theory was set up, which including the principle of pledge loan options, low-carbon, the pledge risk and credit risk control. On this basis, the port logistics pledge loan portfolio under the low-carbon transition optimization model was built up, with pledge loan put option portfolio return, ports and customers, low-carbon structure constraint, single loan VaR pledge rate, pledge loan portfolio average credit risk control conditions. The model solved the drawbacks of existing research focused single port pledge loan and neglecting the pledge loan portfolio under low-carbon transition constraints, etc. [ABSTRACT FROM AUTHOR]

The financial derivatives are financial instruments, that are recently created, and whose main application is to be used as a tool for managing financial derivatives. The most significant financial derivatives are options, that are mostly used for their flexible and non-standard character. Options, and the other financial derivatives, as well, are instruments that are derived from some other financial instruments, that makes them more complicated from one hand, and more risky, from the other hand. Their role is very important for the developing the financial system, and generating economic growth. The subject of research in this paper is the options as a unstandardized financial derivatives, and their basic characteristics and usage in developed, and developing countries. The prime goal is to research the importance of these derivatives in developing countries, with basic focus in the Republic of Macedonia. The results from these paper should suggest if the options are crutial for the developing the Macedonian financial markets. [ABSTRACT FROM AUTHOR]

Wind and solar PV are the most mature forms of renewable energy and are integral to our clean energy strategy. Their intermittency poses technical and economic challenges. Technical challenges are load balancing, frequency regulation, etc. Economic challenges include providing least costing load balancing (reserves) services to these intermittent generators. [ABSTRACT FROM PUBLISHER]

Abstract: We consider an American put option under the CEV process. This corresponds to a free boundary problem for a PDE. We show that this free boundary satisfies a nonlinear integral equation, and analyze it in the limit of small , where is the interest rate and is the volatility. We use perturbation methods to find that the free boundary behaves differently for five ranges of time to expiry. [Copyright &y& Elsevier]

Abstract: Project Tiger has been India''s premier case of conservation success. Since mid 1990s select Project Tiger Reserves in India were chosen for intensive funding by the Global Environment Facility, the International Development Agency (IDA) and the Government of India under the ‘India Eco-Development Project’. This project marked a modest shift towards debt based funding. The GEF Project has become a benchmark for tiger conservation in India both in terms of management outcomes and scale and scope of funding. However in the absence of large-scale budgetary support or self-generating income flows, it becomes difficult for the GEF type of project to be replicated in other tiger reserves of the country. Debt instruments hold promise as enablers of conservation finance. The paper proposes issue of ‘tiger bonds’ to meet the financial requirements of tiger reserves. Though attractive as a debt instrument, a ‘tiger bond’ could nevertheless entail interest rate and default risks. Bioprospecting activities form good revenue sources for tiger reserves to pay off their debts. However bioprospecting activities do not provide assured returns to tiger reserves. Pharmaceutical companies that prospect for genetic resources and practice ‘real options’ approach to R&D investment planning, adopt multi-phased investment systems and sequential searches that gives them the flexibility to abandon R&D projects. From the point of view of genetic resource providing entities like Project Tiger Reserves, the ‘postponement value’ generated by real options, enables a drug company to tap substitutes for the genetic resources that form the subject matter of bioprospecting contracts. To obviate possible repayment risks by tiger reserves, the paper advocates the institution of ‘put bonds’ as a risk management tool for Project Tiger Reserves in order to hedge themselves against loan defaults arising from possible loss in bioprospecting income. The paper also brings out the mechanics of the issue of tiger bonds in the Indian context. It is argued that a put bond not only hedges default risks but would also aid ‘value discovery’ and payment for ecosystem services as far as the Project Tiger Reserves of India are concerned. [Copyright &y& Elsevier]

To coordinate the supply chain risk caused by demand uncertainty, this paper proposed a flexible return strategy under demand uncertainty, in which the retailer can choose return quantity independently by put option after the selling season, while the return quantity is usually determined by the supplier in the classical return strategy. In our novel return strategy, the exercise price is not fixed, and we developed the base model of this strategy, named the selective buyback contracts model. We have solved the optimal pricing and ordering strategies of supply chain members. Numerical studies demonstrated that the contracts can coordinate a supply chain with one retailer and one supplier, and the supplier can adjust the profit distribution of the supply chain by adjusting the option exercise price. Compared with other return strategies, the selective buyback contracts give the retailer more power of choice, and the supplier receives risk compensation from the put options. [ABSTRACT FROM AUTHOR]

In this paper we consider an extension of the single-period inventory model with stochastic demand where a put option can be purchased to reduce losses resulting from low demand. The newsvendor not only chooses the order quantity but also determines the “strike price” and/or the “strike quantity” of the put option. As the buyer of the put option, the newsvendor pays the option writer an amount that equals the expected option payoff plus a risk premium and receives from the option writer the strike price (adjusted for salvage value) for each unit that the demand falls below the strike quantity. The newsvendor is risk-averse and attempts to maximize an expected utility function. We show that: (i) the same order quantity maximizes the expected profit with or without the option; and (ii) the strike price and strike quantity do not affect the newsvendor's maximum expected profit but they do affect the variance of the profit. We use concepts from stochastic dominance theory to prove the following result: if the newsvendor uses the expected profit maximizing order quantity and if she has a quadratic utility function, then maximizing her expected utility is equivalent to minimizing the variance of the profit. Sensitivity analysis results indicate that under poor economic conditions (low sale price/high purchase cost) it may not be optimal to purchase the option. We also find that when the option writer assumes a higher risk/return for the random option payoff (that he pays the newsvendor) the newsvendor can reduce her profit uncertainty by choosing the strike price or strike quantity optimally. [ABSTRACT FROM AUTHOR]

Lookback N -time period performance options are proposed. Explicit risk-neutral probability density functions for extrema of N -time period return rates are obtained over the time interval [0, T ], T ≤ 2 N . Pricing formulae at t = 0 for lookback performance options with logarithm return rate are derived. The pricing formulae for lookback performance options with gross return rate at t = 0 can be derived similarly. Put-call parity relations at t = 0 for these options follow from these pricing formulae. Applications of lookback performance options are also discussed. [ABSTRACT FROM AUTHOR]