Pricing Of Long Dated Commodity Derivatives With Stochastic Volatility And Stochastic Interest Rates
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Pricing Of Long Dated Commodity Derivatives With Stochastic Volatility And Stochastic Interest Rates
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Author : Benjamin Cheng
language : en
Publisher:
Release Date : 2016
Pricing Of Long Dated Commodity Derivatives With Stochastic Volatility And Stochastic Interest Rates written by Benjamin Cheng and has been published by this book supported file pdf, txt, epub, kindle and other format this book has been release on 2016 with categories.
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.
Pricing And Hedging Of Long Dated Commodity Derivatives
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Author : Benjamin Tin Chun Cheng
language : en
Publisher:
Release Date : 2017
Pricing And Hedging Of Long Dated Commodity Derivatives written by Benjamin Tin Chun Cheng and has been published by this book supported file pdf, txt, epub, kindle and other format this book has been release on 2017 with Commodity exchanges categories.
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.
Non Parametric Pricing Of Long Dated Volatility Derivatives Under Stochastic Interest Rates
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Author : Mark S. Joshi
language : en
Publisher:
Release Date : 2015
Non Parametric Pricing Of Long Dated Volatility Derivatives Under Stochastic Interest Rates written by Mark S. Joshi and has been published by this book supported file pdf, txt, epub, kindle and other format this book has been release on 2015 with categories.
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.
Relative Pricing Of Options With Stochastic Volatility
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Author : Olivier Ledoit
language : en
Publisher:
Release Date : 1998
Relative Pricing Of Options With Stochastic Volatility written by Olivier Ledoit and has been published by this book supported file pdf, txt, epub, kindle and other format this book has been release on 1998 with categories.
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.
Pricing Long Maturity Equity And Fx Derivatives With Stochastic Interest Rates And Stochastic Volatility
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Author : Alexander van Haastrecht
language : en
Publisher:
Release Date : 2011
Pricing Long Maturity Equity And Fx Derivatives With Stochastic Interest Rates And Stochastic Volatility written by Alexander van Haastrecht and has been published by this book supported file pdf, txt, epub, kindle and other format this book has been release on 2011 with categories.
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.
Unspanned Stochastic Volatility And The Pricing Of Commodity Derivatives
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Author : Anders B. Trolle
language : en
Publisher:
Release Date : 2016
Unspanned Stochastic Volatility And The Pricing Of Commodity Derivatives written by Anders B. Trolle and has been published by this book supported file pdf, txt, epub, kindle and other format this book has been release on 2016 with categories.
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.
Commodity Derivatives
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Author : Zaizhi Wang
language : en
Publisher:
Release Date : 2011
Commodity Derivatives written by Zaizhi Wang and has been published by this book supported file pdf, txt, epub, kindle and other format this book has been release on 2011 with categories.
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.
Pricing Long Term Options With Stochastic Volatility And Stochastic Interest Rates
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Author : Alexander van Haastrecht
language : en
Publisher:
Release Date : 2010
Pricing Long Term Options With Stochastic Volatility And Stochastic Interest Rates written by Alexander van Haastrecht and has been published by this book supported file pdf, txt, epub, kindle and other format this book has been release on 2010 with categories.
Currency Derivative And International Term Structure Pricing In A Stochastic Interest Rate Stochastic Volatility And Stochastic Jump Intensity World
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Author : Shijun Liu
language : en
Publisher:
Release Date : 2007
Currency Derivative And International Term Structure Pricing In A Stochastic Interest Rate Stochastic Volatility And Stochastic Jump Intensity World written by Shijun Liu and has been published by this book supported file pdf, txt, epub, kindle and other format this book has been release on 2007 with categories.
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.
Commodity Price Dynamics
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Author : Craig Pirrong
language : en
Publisher: Cambridge University Press
Release Date : 2011-10-31
Commodity Price Dynamics written by Craig Pirrong and has been published by Cambridge University Press this book supported file pdf, txt, epub, kindle and other format this book has been release on 2011-10-31 with Business & Economics categories.
Commodities have become an important component of many investors' portfolios and the focus of much political controversy over the past decade. This book utilizes structural models to provide a better understanding of how commodities' prices behave and what drives them. It exploits differences across commodities and examines a variety of predictions of the models to identify where they work and where they fail. The findings of the analysis are useful to scholars, traders and policy makers who want to better understand often puzzling - and extreme - movements in the prices of commodities from aluminium to oil to soybeans to zinc.