Unspanned Stochastic Volatility and the Pricing of Commodity Derivatives PDF Download
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Author: Anders B. Trolle
Publisher:
ISBN:
Category :
Languages : en
Pages : 55
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Book Description
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.
Author: Anders B. Trolle
Publisher:
ISBN:
Category :
Languages : en
Pages : 55
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Book Description
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.
Author: Benjamin Cheng
Publisher:
ISBN:
Category :
Languages : en
Pages : 30
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Book Description
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.
Author: Antoine Petrus Cornelius van der Ploeg
Publisher: Rozenberg Publishers
ISBN: 9051705778
Category :
Languages : en
Pages : 358
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Book Description
Author: Gonzalo Cortazar
Publisher:
ISBN:
Category :
Languages : en
Pages : 60
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Book Description
We propose a novel representation of commodity spot prices in which the cost-of-carry and the spot price volatility are both driven by an arbitrary number of risk factors, nesting many existing specifications. The model exhibits unspanned stochastic volatility, provides simple closed-form expressions of commodity futures, and yields analytic formulas of European options on futures. We estimate the model using oil futures and options data, and find that the pricing of traded contracts is accurate for a wide range of maturities and strike prices. The results suggest that at least three risk factors in the spot price volatility are needed to accurately fit the volatility surface of options on oil futures, highlighting the importance of using general multifactor models in pricing commodity contingent claims.
Author: Benjamin Tin Chun Cheng
Publisher:
ISBN:
Category : Commodity exchanges
Languages : en
Pages : 0
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Book Description
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.
Author: Juan Arismendi-Zambrano
Publisher:
ISBN:
Category :
Languages : en
Pages : 53
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Book Description
Many commodity markets contain a strong seasonal component not only at the price level, but also in volatility. In this paper, the importance of seasonal behavior in the volatility for the pricing of commodity options is analyzed. We propose a seasonally varying long-run mean variance process that is capable of capturing empirically observed patterns. Semi-closed form option valuation formulas are derived. We then empirically study the impact of the proposed seasonal stochastic volatility model on the pricing accuracy of natural gas futures options traded at the New York Mercantile Exchange (NYMEX) and corn futures options traded at the Chicago Board of Trade (CBOT). Our results demonstrate that allowing stochastic volatility to fluctuate seasonally significantly reduces pricing errors for these contracts.
Author: Gregory Pelts
Publisher:
ISBN:
Category :
Languages : en
Pages : 21
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Book Description
For the last decade, short-term rates of major currencies were consistently low and occasionally negative. Meanwhile, longer-term rates remained relatively high and volatile. This phenomenon added extra complexity to the the already formidably difficult task of pricing and hedging interest rate derivatives, rendering conventional approaches virtually defunct. We have observed that the application of jump diffusion in conjunction with conformal geometry allows to successfully tackle such market behavior in a fully consistent, tractable, and computationally efficient manner. The approach provides explicit parametric yield curves with arbitrage-free dynamics, and, in certain cases, even closed-form formulae for yield distributions. This is achieved without compromising efficiency or calibration flexibility. In particular, the 4D version of the model has been successfully calibrated to the swaption market with acceptable precision. The methodology has been applied in valuation of various exotic interest rate derivatives.
Author: Robert A. Jarrow
Publisher:
ISBN:
Category : Derivative securities
Languages : en
Pages : 472
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Book Description
Written by a number of authors, this text is aimed at market practitioners and applies the latest stochastic volatility research findings to the analysis of stock prices. It includes commentary and analysis based on real-life situations.
Author: Ioannis Kyriakou
Publisher:
ISBN:
Category :
Languages : en
Pages : 39
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Book Description
We consider a seasonal mean-reverting model for energy commodity prices with jumps and Heston-type stochastic volatility, as well as three nested models for comparison. By exploiting the affine form of the log-spot models, we develop a general valuation framework for futures and discrete arithmetic Asian options. We investigate five major petroleum commodities from the European market (Brent crude oil, gasoil) and US market (light sweet crude oil, gasoline, heating oil) and analyze the effects of the competing fitted stochastic spot models in futures pricing, Asian options pricing and hedging. We find evidence that price jumps and stochastic volatility are important features of the petroleum price dynamics.
Author: Fred Espen Benth
Publisher: Springer
ISBN: 3319004131
Category : Mathematics
Languages : en
Pages : 326
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Book Description
The current volume presents four chapters touching on some of the most important and modern areas of research in Mathematical Finance: asset price bubbles (by Philip Protter); energy markets (by Fred Espen Benth); investment under transaction costs (by Paolo Guasoni and Johannes Muhle-Karbe); and numerical methods for solving stochastic equations (by Dan Crisan, K. Manolarakis and C. Nee).The Paris-Princeton Lecture Notes on Mathematical Finance, of which this is the fifth volume, publish cutting-edge research in self-contained, expository articles from renowned specialists. The aim is to produce a series of articles that can serve as an introductory reference source for research in the field.
