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This paper describes a method for computing risk-neutral density functions based on the option-implied volatility smile. Its aim is to reduce complexity and provide cookbook-style guidance through the estimation process. The technique is robust and avoids violations of option no-arbitrage restrictions that can lead to negative probabilities and other implausible results. I give examples for equities, foreign exchange, and long-term interest rates.
This paper describes a method of extracting the risk-neutral probability distribution of future exchange rates from option prices. In foreign exchange markets interbank option pricing conventions make possible reliable inferences about risk-neutral probability distributions with relatively little data. Moments drawn from risk-neutral exchange rate distribution are used to explore several issues related to the puzzle of excess returns in currency markets. Tests of the international capital asset pricing model using risk-neutral moments as explanatory variables indicate that option-based moments have considerably greater explanatory power for excess returns in currency markets than has been found in earlier work. Tests of several hypotheses generated by the peso problem approach indicate that jump risk measured by the risk-neutral coefficient of skewness can explain only a small part of the forward bias. These tests take into account not only the second, but the third and fourth moments of the exchange rate implied by option prices, and avoid testing a joint hypothesis including a distributional assumption.
This paper derives exact formulas for retrieving risk neutral moments of future payoffs of any order from generic European-style option prices. It also provides an exact formula for retrieving the expected quadratic variation of the stock market implied by European option prices, which nowadays is used as an estimate of the implied volatility, and a formula approximating the jump component of this measure of variation. To implement the above formulas to discrete sets of option prices, the paper suggests a numerical procedure and provides upper bounds of its approximation errors. The performance of this procedure is evaluated through a simulation and an empirical exercise. Both of these exercises clearly indicate that the suggested numerical procedure can provide accurate estimates of the risk neutral moments, over different horizons ahead. These can be in turn employed to obtain accurate estimates of risk neutral densities and calculate option prices, efficiently, in a model-free manner. The paper also shows that, in contrast to the prevailing view, ignoring the jump component of the underlying asset can lead to seriously biased estimates of the new volatility index suggested by the Chicago Board Options Exchange (CBOE).
A clear new finance textbook that explains essential models and practices, and how the financial world works now Contemporary Financial Markets and Institutions: Tools and Techniques to Manage Risk and Uncertainty is an ideal introduction to finance for professionals and students. It covers the basic finance theory required to understand the contemporary financial world and builds on it to present finance in a detailed yet comprehensible way. It explains markets and institutions, and the central bank and government policies that influence how they operate. The book begins with an overview of basic finance theory, including investments, asset return behavior, derivatives pricing, and credit risk. It discusses topics that have dominated markets in recent decades, such as extreme events, liquidity, currency and debt crises, and radical changes in monetary policy and regulation. The concepts are presented alongside examples, strange market episodes, and data from recent experience. Contemporary Financial Markets and Institutions covers advanced credit topics like securitization in a straightforward, succinct way, without advanced mathematics, but with detailed examples using real market data. It integrates financial and macroeconomic content seamlessly. The book is suitable for use by undergraduate and graduate students, and by practitioners of all backgrounds. Abundant pedagogical resources in the book and online facilitate pedagogy. Learn the basic concepts and models in finance, including investment, asset pricing, uncertainty and risk, monetary policy and the regulatory system Explore recent developments, from the expansion of central banks to the chaos in commercial banking to changes in financial technology, that are dominating markets worldwide Gain knowledge of risk types, models, and measurement methods, and the impact of regulation Prepare yourself for a successful career in finance, or update your existing knowledge base with this comprehensive reference guide Ideal as a sole or supplementary textbook for beginning and advanced finance courses, as well as for practitioners in finance-related fields, this book takes a unique, market-focused approach that will serve readers well in our turbulent and puzzling times.
This comprehensive guide offers traders, quants, and students the tools and techniques for using advanced models for pricing options. The accompanying website includes data files, such as options prices, stock prices, or index prices, as well as all of the codes needed to use the option and volatility models described in the book. Praise for Option Pricing Models & Volatility Using Excel-VBA "Excel is already a great pedagogical tool for teaching option valuation and risk management. But the VBA routines in this book elevate Excel to an industrial-strength financial engineering toolbox. I have no doubt that it will become hugely successful as a reference for option traders and risk managers." —Peter Christoffersen, Associate Professor of Finance, Desautels Faculty of Management, McGill University "This book is filled with methodology and techniques on how to implement option pricing and volatility models in VBA. The book takes an in-depth look into how to implement the Heston and Heston and Nandi models and includes an entire chapter on parameter estimation, but this is just the tip of the iceberg. Everyone interested in derivatives should have this book in their personal library." —Espen Gaarder Haug, option trader, philosopher, and author of Derivatives Models on Models "I am impressed. This is an important book because it is the first book to cover the modern generation of option models, including stochastic volatility and GARCH." —Steven L. Heston, Assistant Professor of Finance, R.H. Smith School of Business, University of Maryland
In Volatility Trading, Sinclair offers you a quantitative model for measuring volatility in order to gain an edge in your everyday option trading endeavors. With an accessible, straightforward approach. He guides traders through the basics of option pricing, volatility measurement, hedging, money management, and trade evaluation. In addition, Sinclair explains the often-overlooked psychological aspects of trading, revealing both how behavioral psychology can create market conditions traders can take advantage of-and how it can lead them astray. Psychological biases, he asserts, are probably the drivers behind most sources of edge available to a volatility trader. Your goal, Sinclair explains, must be clearly defined and easily expressed-if you cannot explain it in one sentence, you probably aren't completely clear about what it is. The same applies to your statistical edge. If you do not know exactly what your edge is, you shouldn't trade. He shows how, in addition to the numerical evaluation of a potential trade, you should be able to identify and evaluate the reason why implied volatility is priced where it is, that is, why an edge exists. This means it is also necessary to be on top of recent news stories, sector trends, and behavioral psychology. Finally, Sinclair underscores why trades need to be sized correctly, which means that each trade is evaluated according to its projected return and risk in the overall context of your goals. As the author concludes, while we also need to pay attention to seemingly mundane things like having good execution software, a comfortable office, and getting enough sleep, it is knowledge that is the ultimate source of edge. So, all else being equal, the trader with the greater knowledge will be the more successful. This book, and its companion CD-ROM, will provide that knowledge. The CD-ROM includes spreadsheets designed to help you forecast volatility and evaluate trades together with simulation engines.
A strand of research documents Chile’s copper dependence hence significant exposure to terms of trade shocks. Copper prices’ sharp decline and forecast uncertainty since the end of the commodity super-cycle has rekindled the debate on Chile’s adjustment capacity to external shocks. Following Malz (2014), this paper builds a time-varying measure of copper price uncertainty using options contracts. VAR analysis shows that the investment response to an uncertainty shock of average magnitude in the sample is strong and persistent: the cumulative fall in investment from trend at a one-year horizon ranges 2–5.8 percentage points; and it takes between 11⁄2 and 2 years for investment to return to its trend level. Empirical ranges depend on alternative definitions for investment, uncertainty, and options’ maturing time.