Lognormal vs Normal Volatilities and Sensitivities in Practice

On the Information in the Interest Rate Term Structure and Option Prices

Summaries of Papers In This Issue

This paper studies the effects of U.S. unconventional monetary policy announcements on the implied volatility of three major currency pairs, Dollar/Euro, Dollar/British Pound and Dollar/Yen by using panel data analysis along with several model specifications and robustness tests. Monetary policy announcements not only have an effect on the realized behavior of asset prices, but also influence market participants’ expectations regarding future volatility. Our empirical findings show that Federal Reserve’s unconventional monetary policy announcements significantly reduce the market expectations about future realized volatility of exchange rates, suggesting that lax monetary policy leads to elevated risk-tolerance in currency markets. Furthermore, our findings indicate that market participants’ expectations respond differently to the different rounds of U.S. quantitative easing.

Return Dynamics With Lévy Jumps: Evidence from Stock and Option Prices

Rough Heston model possesses some stylized facts that can be used to describe the stock market, i.e., markets are highly endogenous, no statistical arbitrage mechanism, liquidity asymmetry for buy and sell order, and the presence of metaorders. This paper presents an efficient alternative to compute option prices under the rough Heston model. Through the decomposition formula of the option price under the rough Heston model, we manage to obtain an approximation formula for option prices that is simpler to compute and requires less computational effort than the Fourier inversion method. In addition, we establish finite error bounds of approximation formula of option prices under the rough Heston model for 0.1≤H<0.5 under a simple assumption. Then, the second part of the work focuses on the short-time implied volatility behavior where we use a second-order approximation on the implied volatility to match the terms of Taylor expansion of call option prices. One of the key results that we manage to obtain is that the second-order approximation for implied volatility (derived by matching coefficients of the Taylor expansion) possesses explosive behavior for the short-time term structure of at-the-money implied volatility skew, which is also present in the short-time option prices under rough Heston dynamics. Numerical experiments were conducted to verify the effectiveness of the approximation formula of option prices and the formulas for the short-time term structure of at-the-money implied volatility skew.

Correlating Market Models

Bermudan swaptions are options on interest rate swaps which can be exercised on one or more dates before the final maturity of the swap. Because the exercise boundary between the continuation area and stopping area is inherently complex and multi-dimensional for interest rate products, there is an inherent “tug of war” between the pursuit of calibration and pricing precision, tractability, and implementation efficiency. After reviewing the main ideas and implementation techniques underlying both single- and multi-factor models, we offer our own approach based on dimension reduction via Markovian projection. Specifically, on the theoretical side, we provide a reinterpretation and extension of the classic result due to Gyöngy which covers non-probabilistic, discounted, distributions relevant in option pricing. Thus, we show that for purposes of swaption pricing, a potentially complex and multidimensional process for the underlying swap rate can be collapsed to a one-dimensional one. The empirical contribution of the paper consists in demonstrating that even though we only match the marginal distributions of the two processes, Bermudan swaptions prices calculated using such an approach appear well-behaved and closely aligned to counterparts from more sophisticated models.

18 - The Eurobond market I

Fractional Brownian motion in option pricing and dynamic delta hedging: Experimental simulations

The Indonesian stock market, especially PT Bank Central Asia (BCA) stock experiences high volatility. Therefore, this research is very important to provide a deeper understanding of the pricing of put and call options as a risk management instrument. This study aims to analyze the pricing of put and call options on PT Bank Central Asia (BCA) shares using the Black-Scholes model and identify factors that affect stock price fluctuations on option prices. This study aims to understand the changes in put and call option prices on PT Bank Central Asia (BCA) shares caused by fluctuations in stock prices. This study uses historical data of PT Bank Central Asia (BCA) shares, volatility, and current interest rates as the basis for analysis. The Black-Scholes method is used as a framework to analyze the pricing of put and call options by considering volatility and interest rates. The results of this study analyze the price changes of put and call options in the face of stock price fluctuations and the factors that affect option prices so as to provide insight into risk management and investment decision making. This research is expected to provide practical guidance for investors and risk managers in making decisions related to put and call options on PT Bank Central Asia (BCA) shares.

Option pricing is essential for market participants as it facilitates risk management and price discovery. This study provides a comprehensive elucidation of diverse option pricing models. The author delineates the development of option pricing models from the fundamental Black-Scholes-Merton model (BSM) to more intricate methodologies. The importance of comprehending option pricing for hedging strategies and risk management is crucial in financial mathematics. The study analyses several models, including the BS model, Jump Diffusion model (JDM), Binomial Tree model (BTM), Monte Carlo simulation (MCS), and stochastic volatility models (SVM), while addressing their applications, limitations, advantages, and disadvantages. This work delineates the history and distinctions between other models and the Black-Scholes-Merton model. The Black-Scholes-Merton model exerts the most substantial influence on financial markets. The alternative models exhibit greater flexibility and enhanced accuracy when confronting complicated and uncertain market trends. The trend of future development is bound to be the continuous updating of models to adapt to more complex situations.

Volume visualization of derivatives helps us discover risks, which hitherto have been elusive with traditional surface plots. In this paper, we would like to address the volatility visualization issue, which is one of the critical components in Option pricing, by incorporating volume visualization for better risk management. By enabling the visualization of volatility changes in risk profiling, combining with another two Option’s value determinants (i.e. the underlying asset spot price and days to maturity), a much better understanding about the risk involved in a portfolio can be achieved, particularly when the fluctuation of the asset is highly uncertain.

Introduction. One of the peculiarities of Ukrainian agrarian market functioning is the growth of uncertainties, whose impact has increased significantly as a result of globalization processes. The constant change of external and internal factors causes risks, which become the main problem of management, as they determine the directions and production efficiency and agricultural products sale. Therefore, there is a need to apply progressive risk management methods and tools that are effective and efficient under current conditions. Companies use derivatives (trusted derivatives) to turn their cases around and limit uncertainty about future businesses for revitalization. Therefore, derivatives are actually invested in some economies and make their effectiveness for a higher level of valuable assets in the course of exchange trading. The purpose of the article is to substantiate scientifically theoretical positions and methodological approaches, to develop alternative risk management strategies through stock exchange instruments, namely types of derivatives – options. Results. The importance of theoretical bases formation of the risk essence is substantiated that can be faced by domestic producers. The ways of uncertainties occurrence, stages of their transformation are explained. The theoretical approach to risk management through the use of futures contracts is systematized. The historical stages of using derivatives development have been evaluated. The new approach to risk management is proposed through the use of the optional Collar strategy. Conclusions. Any business activity is unthinkable without risks in developed countries, so any manufacturer seeks to insure its risk, including through a fixed market. The terminal market allows for redistribution of risks among market participants, on which a particular derivative operates. The advantage of derivatives is the leverage that allows participants to operate large amounts of risk management funds, including hedging their own products. Keywords: risk, risk management, risk management, hedges, options, futures, derivatives, derivatives.

Nothing else has as strong an influence on success in the planning and execution of a Public Private Partnership (PPP) as the identification, evaluation, allocation and controlling of risk. Yet risk management of PPP remains largely unexplored. For many market participants, great uncertainty prevails in the management of risk. The choices for cost and quality assurance through active control of risks are scarcely known and have not been exhausted adequately. Experiences gained in PPP pilot projects also show that risk management is performed more on a periodic basis instead of dealing with risks consistently. For the optimisation of future PPP projects, a professional approach to risk management has become a necessity in order to reduce the existing complexity. This paper emphasises the significance of risk in life cycle oriented real estate projects, which is most clearly present in long-term contractual arrangements. The risk involved in a project needs to be calculated for the entire project life cycle and accordingly, risk must be controlled throughout this period. Additionally, every step of the value chain such as planning, construction, financing, maintenance, and operation involves specific risk factors. Due to the diverse perspectives and exposures to risk among the participants, this paper will pay special attention to the balancing of the respective interests of the participants. Their differing objectives, functions, risk perception, risk bearing capability affect the process and structure in dealing with risk. As a consequence, each party might implement different kinds of strategies to manage project risks and hence influence the cost effectiveness of the project. Great attention needs to therefore be paid by all of those who are involved in the project. In addition to the risk related characteristics of the project life cycle and the stakeholder perspectives, this paper explores the steps of a risk management process and presents a comprehensive concept which implements all of these critical areas as a basis for further advancements. The author argues for a higher general risk awareness and further aims to present potential for the implementation of a sustainable risk management framework over the entire life cycle of a PPP project in real estate.

This paper investigates the approximated arbitrage bounds of option prices in an incomplete market setting and draws implications for option pricing and risk management. It gives consideration to periods of global financial crisis and European sovereign debt crisis. To this end, we employ the gain-loss ratio method combined with the market-implied risk-neutral distribution calculated by binomial tree to investigate the options price bounds. Our implied gain-loss bounds of option prices are preference-free and parametric-free to avoid the misspecification error of subjective choice on the benchmark model of gain-loss ratio, and consequently, greatly reduce model risk and market risk. The empirical results show that there are option prices breaking the gain-loss bounds, even after taking into account the market information. This means that a good risk management technique and good-deal investment opportunities exist if the implied binomial tree is used as a benchmark model in the gain-loss bounds.