Exchange Options
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Author(s):  
Tumellano Sebehela

The interdependence of options is common among compound options. Moreover, this interconnectedness is synonymous with probability theory-how a set of axioms are treated. The conditionality, where one option value is dependent on another option, has spilled over to option pricing, especially exchange options. However, it seems that no study has explored whether that simultaneous occurrence of two options is conditional or not. This study uses conditional approaches (Radon–Nikodým derivative and probability theory) to illustrate conditionality in an exchange option. Furthermore, hedging strategy is derived based on straddles. The results show that due to conditionality another exotic option, tri-conditional option (also known as triple option) is derived. The hedging of a triple option encompasses both dynamic and static techniques.


Author(s):  
Elena Starchenko ◽  
Danil Verzhitskii

Introduction. The choice and justification of options for attracting investments are relevant for the development of any organization. The research objective was to assess exchange-traded options for attracting investment by small and medium businesses in the food and processing industry. Study objects and methods. The research featured small and medium businesses in the food and processing industry and their exchange options for attracting external financing. The study was based on system, situational, structural-functional, and process approaches, as well as methods of comparative and factor analysis, grouping, and sociological research techniques. Results and discussion. The authors described, analyzed, and classified ways to attract external financing by small and medium businesses. Exchange-traded options proved to be associated with the circulation of securities that differ in liquidity, direct access to the owners of funds, and access to a potentially unlimited amount of investment capital. The authors analyzed the existing exchange infrastructure for the businesses under consideration and assessed their potential for issuing securities. Based on such indicators as Average EBIT Margin and Compound Annual Growth Rate (CAGR), small and medium food-related enterprises can issuer securities, especially exchange-traded bonds. Exchange-traded bonds demonstrated a number of serious disadvantages, compared to a traditional bank loan. However, issuers of securities receive guaranteed advantages, e.g. more flexible conditions for raising funds on the exchange, the right to state subsidies for the payment of coupon income, partial compensation for the costs of placing securities, the absence of collateral, a wide range of private investors, etc. Using some real cases, the authors evaluated the liquidity of exchange-traded bonds of small and medium businesses in the food and processing industry according to a number of indicators of profitability and liquidity of securities. Conclusion. Exchange options can be used to finance small and medium food-related businesses, based on the established ex-change infrastructure, government incentives, potential of the food sector, average EBIT profitability, and revenue growth.


Author(s):  
Tumellano Sebehela

The stock jumps of the underlying assets underpinning the Margrabe options have been studied by Cheang and Chiarella [Cheang, GH and Chiarella C (2011). Exchange options under jump-diffusion dynamics. Applied Mathematical Finance, 18(3), 245–276], Cheang and Garces [Cheang, GHL and Garces LPDM (2020). Representation of exchange option prices under stochastic volatility jump-diffusion dynamics. Quantitative Finance, 20(2), 291–310], Cufaro Petroni and Sabino [Cufaro Petroni, N and Sabino P (2020). Pricing exchange options with correlated jump diffusion processes. Quantitate Finance, 20(11), 1811–1823], and Ma et al. [Ma, Y, Pan D and Wang T (2020). Exchange options under clustered jump dynamics. Quantitative Finance, 20(6), 949–967]. Although the authors argue that they explored stock jumps under Hawkes processes, those processes are the Poisson process in their applications. Thus, they studied Hawkes processes in-between two assets while this study explores Hawkes process within any asset. Furthermore, the Poisson process can be flipped into Hawkes process and vice versa. In terms of hedging, this study uses specific Greeks (rho and phi) while some of the mentioned studies used other Greeks (Delta, Theta, Vega, and Gamma). Moreover, hedging is carried out under static and dynamic environments. The results illustrate that the jumpy Margrabe option can be extended to complex barrier option and waiting to invest option. In addition, hedging strategies are robust both under static and dynamic environments.


Author(s):  
Huahua Li ◽  
Lihan Gu

The current relevant models for the analysis of SSE options, whether for the study of theoretical algorithms or for the application of verification, are still at the beginning of the research stage. Based on this, this study combines the status quo of China’s SSE options to construct a state space model with certain flexibility and combines image processing technology to extract model features. At the same time, this study obtained the experimental data of this study through network data collection method and analyzed the performance of the algorithm by comparison method, recorded the data obtained by the model operation, and turned the result into a visually identifiable feature result through image processing. The research indicates that the state space model has certain effects in the analysis of SSE option and can provide theoretical reference for subsequent related research.


Author(s):  
Puneet Pasricha ◽  
Anubha Goel

This article derives a closed-form pricing formula for the European exchange option in a stochastic volatility framework. Firstly, with the Feynman–Kac theorem's application, we obtain a relation between the price of the European exchange option and a European vanilla call option with unit strike price under a doubly stochastic volatility model. Then, we obtain the closed-form solution for the vanilla option using the characteristic function. A key distinguishing feature of the proposed simplified approach is that it does not require a change of numeraire in contrast with the usual methods to price exchange options. Finally, through numerical experiments, the accuracy of the newly derived formula is verified by comparing with the results obtained using Monte Carlo simulations.


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