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Pricing Of Long Dated Commodity Derivatives With Stochastic Volatility And Stochastic Interest Rates
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Book Synopsis Pricing of Long-Dated Commodity Derivatives with Stochastic Volatility and Stochastic Interest Rates by : Benjamin Cheng
Download or read book Pricing of Long-Dated Commodity Derivatives with Stochastic Volatility and Stochastic Interest Rates written by Benjamin Cheng and published by . This book was released on 2016 with total page 30 pages. Available in PDF, EPUB and Kindle. Book excerpt: Aiming to study pricing of long-dated commodity derivatives, this paper presents a class of models within the Heath, Jarrow, and Morton (1992) framework for commodity futures prices that incorporates stochastic volatility and stochastic interest rate and allows a correlation structure between the futures price process, the futures volatility process and the interest rate process. The functional form of the futures price volatility is specified so that the model admits finite dimensional realisations and retains affine representations, henceforth quasi-analytical European futures option pricing formulae can be obtained. A sensitivity analysis reveals that the correlation between the interest rate process and the futures price process has noticeable impact on the prices of long-dated futures options, while the correlation between the interest rate process and the futures price volatility process does not impact option prices. Furthermore, when interest rates are negatively correlated with futures prices then option prices are more sensitive to the volatility of interest rates, an effect that is more pronounced with longer maturity options.
Book Synopsis Pricing and Hedging of Long-dated Commodity Derivatives by : Benjamin Tin Chun Cheng
Download or read book Pricing and Hedging of Long-dated Commodity Derivatives written by Benjamin Tin Chun Cheng and published by . This book was released on 2017 with total page 0 pages. Available in PDF, EPUB and Kindle. Book excerpt: Commodity markets have grown substantially over the last decade and significantly contribute to all major financial sectors such as hedge funds, investment funds and insurance. Crude oil derivatives, in particular, are the most actively traded commodity derivative in which the market for long-dated contracts have tripled over the last 10 years. Given the rapid development and increasing importance of long-dated commodity derivatives contracts, models that can accurately evaluate and hedge this type of contracts become of critical importance. The main contributions of this thesis include: Pricing of long-dated commodity derivatives with stochastic volatility and stochastic interest rates; Empirical pricing performance on long-dated crude oil derivatives; Hedging of futures options with stochastic interest rates; and Empirical hedging performance on long-dated crude oil derivatives.
Book Synopsis Non-Parametric Pricing of Long-Dated Volatility Derivatives Under Stochastic Interest Rates by : Mark S. Joshi
Download or read book Non-Parametric Pricing of Long-Dated Volatility Derivatives Under Stochastic Interest Rates written by Mark S. Joshi and published by . This book was released on 2015 with total page 25 pages. Available in PDF, EPUB and Kindle. Book excerpt: Although the effect of interest rate stochasticity can safely be ignored for short-dated exchange traded volatility derivatives, this is not the case for the kind of long-dated OTC derivatives often used by insurance companies and other financial institutions. We therefore extend existing model-free results for the pricing of variance swaps and more general volatility derivatives to account for stochastic interest rates, given certain independence and continuity assumptions. Finally, we present empirical examples to highlight the potential significance of this effect on long term contracts.
Book Synopsis Relative Pricing of Options with Stochastic Volatility by : Olivier Ledoit
Download or read book Relative Pricing of Options with Stochastic Volatility written by Olivier Ledoit and published by . This book was released on 1998 with total page 11 pages. Available in PDF, EPUB and Kindle. Book excerpt: This paper offers a new approach for pricing options on assets with stochastic volatility. We start by constructing the quot;surfacequot; of Black-Scholes implied volatilities for (readily observable) liquid, European call options with varying strike prices and maturities. Then, we show that the implied volatility of an at-the-money call option with time-to-maturity going tozero is equal to the underlying asset's instantaneous (stochastic) volatility. We then model the stochastic processes followed by the implied volatilities of options of all maturities and strike prices jointly with the stock price, and find a no-arbitrage condition that their drift must satisfy. Finally, we use the resulting arbitrage-free joint process for the stock price and its volatility to price other derivatives, such as standard but illiquid options as well as exotic options using numerical methods. The great advantage of our approach is that, when pricing these other derivatives, we are secure in the knowledge that the model values the hedging instruments - namely the stock and the simple, liquid options - consistently with the market. Our approach can easily be extended to allow for stochastic interest rates and a stochastic dividend yield, which may be particularly relevant to the pricing of currency and commodity options. We can also extend our model to price bond options when the term structure of interest rates has stochastic volatility.
Author :Antoine Petrus Cornelius van der Ploeg Publisher :Rozenberg Publishers ISBN 13 :9051705778 Total Pages :358 pages Book Rating :4.0/5 (517 download)
Book Synopsis Stochastic volatility and the pricing of financial derivatives by : Antoine Petrus Cornelius van der Ploeg
Download or read book Stochastic volatility and the pricing of financial derivatives written by Antoine Petrus Cornelius van der Ploeg and published by Rozenberg Publishers. This book was released on 2006 with total page 358 pages. Available in PDF, EPUB and Kindle. Book excerpt:
Book Synopsis Pricing Long-Maturity Equity and FX Derivatives with Stochastic Interest Rates and Stochastic Volatility by : Alexander van Haastrecht
Download or read book Pricing Long-Maturity Equity and FX Derivatives with Stochastic Interest Rates and Stochastic Volatility written by Alexander van Haastrecht and published by . This book was released on 2011 with total page 28 pages. Available in PDF, EPUB and Kindle. Book excerpt: In this paper we extend the stochastic volatility model of Schouml;bel and Zhu (1999) by including stochastic interest rates. Furthermore we allow all driving model factors to be instantaneously correlated with each other, i.e. we allow for a correlation between the instantaneous interest rates, the volatilities and the underlying stock returns. By deriving the characteristic function of the log-asset price distribution, we are able to price European stock options in closed-form by Fourier inversion. Furthermore we present a Foreign Exchange generalization and show how the pricing of Forward-starting options like cliquets can be performed. Additionally we discuss the practical implementation of these new models.
Book Synopsis Financial Derivatives Pricing by : Robert A. Jarrow
Download or read book Financial Derivatives Pricing written by Robert A. Jarrow and published by World Scientific. This book was released on 2008 with total page 609 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book is a collection of original papers by Robert Jarrow that contributed to significant advances in financial economics. Divided into three parts, Part I concerns option pricing theory and its foundations. The papers here deal with the famous Black-Scholes-Merton model, characterizations of the American put option, and the first applications of arbitrage pricing theory to market manipulation and liquidity risk.Part II relates to pricing derivatives under stochastic interest rates. Included is the paper introducing the famous Heath?Jarrow?Morton (HJM) model, together with papers on topics like the characterization of the difference between forward and futures prices, the forward price martingale measure, and applications of the HJM model to foreign currencies and commodities.Part III deals with the pricing of financial derivatives considering both stochastic interest rates and the likelihood of default. Papers cover the reduced form credit risk model, in particular the original Jarrow and Turnbull model, the Markov model for credit rating transitions, counterparty risk, and diversifiable default risk.
Book Synopsis Stochastic Models for Prices Dynamics in Energy and Commodity Markets by : Fred Espen Benth
Download or read book Stochastic Models for Prices Dynamics in Energy and Commodity Markets written by Fred Espen Benth and published by Springer Nature. This book was released on 2023-11-16 with total page 250 pages. Available in PDF, EPUB and Kindle. Book excerpt: This monograph presents a theory for random field models in time and space, viewed as stochastic processes with values in a Hilbert space, to model the stochastic dynamics of forward and futures prices in energy, power, and commodity markets. In this book, the well-known Heath–Jarrow–Morton approach from interest rate theory is adopted and extended into an infinite-dimensional framework, allowing for flexible modeling of price stochasticity across time and along the term structure curve. Various models are introduced based on stochastic partial differential equations with infinite-dimensional Lévy processes as noise drivers, emphasizing random fields described by low-dimensional parametric covariance functions instead of classical high-dimensional factor models. The Filipović space, a separable Hilbert space of Sobolev type, is found to be a convenient state space for the dynamics of forward and futures term structures. The monograph provides a classification of important operators in this space, covering covariance operators and the stochastic modeling of volatility term structures, including the Samuelson effect. Fourier methods are employed to price many derivatives of interest in energy, power, and commodity markets, and sensitivity 'delta' expressions can be derived. Additionally, the monograph covers forward curve smoothing, the connection between forwards with fixed delivery and delivery period, as well as the classical theory of forward and futures pricing. This monograph will appeal to researchers and graduate students interested in mathematical finance and stochastic analysis applied in the challenging markets of energy, power, and commodities. Practitioners seeking sophisticated yet flexible and analytically tractable risk models will also find it valuable.
Book Synopsis Commodity Derivatives by : Zaizhi Wang
Download or read book Commodity Derivatives written by Zaizhi Wang and published by . This book was released on 2011 with total page 139 pages. Available in PDF, EPUB and Kindle. Book excerpt: Commodity prices have been rising at an unprecedented pace over the last years making commodity derivatives more and more popular in many sectors like energy, metals and agricultural products. The quick development of commodity market as well as commodity derivative market results in a continuously uprising demand of accuracy and consistency in commodity derivative modeling and pricing. The specification of commodity modeling is often reduced to an appropriate representation of convenience yield, intrinsic seasonality and mean reversion of commodity price. As a matter of fact, convenience yield can be extracted from forward strip curve and then be added as a drift term into pricing models such as Black Scholes model, local volatility model and stochastic volatility model. Besides those common models, some specific commodity models specially emphasize on the importance of convenience yield, seasonality or mean reversion feature. By giving the stochasticity to convenience yield, Gibson Schwartz model interprets the term structure of convenience yield directly in its model parameters, which makes the model extremely popular amongst researchers and market practitioners in commodity pricing. Gabillon model, in the other hand, focuses on the feature of seasonality and mean reversion, adding a stochastic long term price to correlate spot price. In this thesis, we prove that there is mathematical equivalence relation between Gibson Schwartz model and Gabillon model. Moreover, inspired by the idea of Gyöngy, we show that Gibson Schwartz model and Gabillon model can reduce to one-factor model with explicitly calculated marginal distribution under certain conditions, which contributes to find the analytic formulas for forward and vanilla options. Some of these formulas are new to our knowledge and other formulas confirm with the earlier results of other researchers. Indeed convenience yield, seasonality and mean reversion play a very important role, but for accurate pricing, hedging and risk management, it is also critical to have a good modeling of the dynamics of volatility in commodity markets as this market has very fluctuating volatility dynamics. While the formers (seasonality, mean reversion and convenience yield) have been highly emphasized in the literature on commodity derivatives pricing, the latter (the dynamics of the volatility) has often been forgotten. The family of stochastic volatility model is introduced to strengthen the dynamics of the volatility, capturing the dynamic smile of volatility surface thanks to a stochastic process on volatility itself. It is a very important characteristic for pricing derivatives of long maturity. Stochastic volatility model also corrects the problem of opposite underlying-volatility correlation against market data in many other models by introducing correlation parameter explicitly. The most popular stochastic volatility models include Heston model, Piterbarg model, SABR model, etc. As pointed out by Piterbarg, the need of time-dependent parameters in stochastic volatility models is real and serious. It is because in one hand stochastic volatility models with constant parameters are generally incapable of fitting market prices across option expiries, and in the other hand exotics do not only depend on the distribution of the underlying at the expiry, but on its dynamics through all time. This contradiction implies the necessity of time-dependent parameters. In this thesis, we extend Piterbarg's idea to the whole family of stochastic volatility model, making all the stochastic volatility models having time-dependent parameters and show various formulas for vanilla option price by employing various techniques such as characteristic function, Fourier transform, small error perturbation, parameter averaging, etc.
Book Synopsis Pricing of Options on Commodity Futures with Stochastic Term Structures of Convenience Yields and Interest Rates by : Kristian R. Miltersen
Download or read book Pricing of Options on Commodity Futures with Stochastic Term Structures of Convenience Yields and Interest Rates written by Kristian R. Miltersen and published by . This book was released on 1997 with total page 40 pages. Available in PDF, EPUB and Kindle. Book excerpt:
Book Synopsis Derivatives, Risk Management & Value by : Mondher Bellalah
Download or read book Derivatives, Risk Management & Value written by Mondher Bellalah and published by World Scientific. This book was released on 2009-05-01 with total page 996 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book covers fundamental concepts in financial markets and asset pricing such as hedging, arbitrage, speculation in different markets, classical models for pricing of simple and complex derivatives, mathematical foundations, managing and monitoring portfolios of derivatives in real time, etc. It explains different applications of these concepts using real world examples. The book also covers topics like financial markets and instruments, option pricing models, option pricing theory, exotic derivatives, second generation options, etc.Written in a simple manner and amply supported by real world examples, questions and exercises, the book will be of interest to students, academics and practitioners alike.
Book Synopsis Pricing Long-term Options with Stochastic Volatility and Stochastic Interest Rates by : Alexander van Haastrecht
Download or read book Pricing Long-term Options with Stochastic Volatility and Stochastic Interest Rates written by Alexander van Haastrecht and published by . This book was released on 2010 with total page 231 pages. Available in PDF, EPUB and Kindle. Book excerpt:
Book Synopsis A Simplified Discrete Time Approach for the Pricing of Derivative Securities with Stochastic Interest Rates by : Kaushik I. Amin
Download or read book A Simplified Discrete Time Approach for the Pricing of Derivative Securities with Stochastic Interest Rates written by Kaushik I. Amin and published by . This book was released on 1990 with total page 68 pages. Available in PDF, EPUB and Kindle. Book excerpt:
Book Synopsis Unspanned Stochastic Volatility and the Pricing of Commodity Derivatives by : Anders B. Trolle
Download or read book Unspanned Stochastic Volatility and the Pricing of Commodity Derivatives written by Anders B. Trolle and published by . This book was released on 2016 with total page 55 pages. Available in PDF, EPUB and Kindle. Book excerpt: Commodity derivatives are becoming an increasingly important part of the global derivatives market. Here we develop a tractable stochastic volatility model for pricing commodity derivatives. The model features unspanned stochastic volatility, quasi-analytical prices of options on futures contracts, and dynamics of the futures curve in terms of a low-dimensional affine state vector. We estimate the model on NYMEX crude oil derivatives using an extensive panel data set of 45,517 futures prices and 233,104 option prices, spanning 4082 business days. We find strong evidence for two, predominantly unspanned, volatility factors.
Book Synopsis Derivatives Pricing and Modeling by : Jonathan Batten
Download or read book Derivatives Pricing and Modeling written by Jonathan Batten and published by Emerald Group Publishing. This book was released on 2012-07-02 with total page 446 pages. Available in PDF, EPUB and Kindle. Book excerpt: Highlights research in derivatives modelling and markets in a post-crisis world across a number of dimensions or themes. This book addresses the following main areas: derivatives models and pricing, model application and performance backtesting, and new products and market features.
Book Synopsis A Maximal Stochastic Volatility Model for Commodity Prices by : Walker Keener Hughen
Download or read book A Maximal Stochastic Volatility Model for Commodity Prices written by Walker Keener Hughen and published by . This book was released on 2007 with total page 208 pages. Available in PDF, EPUB and Kindle. Book excerpt:
Book Synopsis Currency Derivative and International Term Structure Pricing in a Stochastic Interest Rate, Stochastic Volatility and Stochastic Jump Intensity World by : Shijun Liu
Download or read book Currency Derivative and International Term Structure Pricing in a Stochastic Interest Rate, Stochastic Volatility and Stochastic Jump Intensity World written by Shijun Liu and published by . This book was released on 2007 with total page 37 pages. Available in PDF, EPUB and Kindle. Book excerpt: We first derive closed form solutions for currency options, currency futures, future options and the term structures of interest rates in a diffusion-jump model of stochastic interest rate, stochastic volatility and time varying jump intensity in currency price. We demonstrate that the introduction of constant jump intensity in the nominal stochastic discount factor shifts the whole term structure of interest rates vertically but has no influence on its shape. However, when the jump intensity is endogenous (time varying) the shape of the term structure is influenced through the factor sensitivity of interest rates. We also document considerable improvement in currency option pricing precision over alternative models if the true model is diffusion-jump with endogenous intensity in a simulation experiment. We conclude that allowing for multidimensional interaction is of significant qualitative and quantitative importance for the pricing of currency options and for understanding the shape of the term structure.
