Advances in pricing commodity futures: Multifactor models
نویسندگان
چکیده
In recent years commodity markets have experienced a dramatic growth in trading volume, the variety of contracts and underlying commodities. Futures as well as forward are contracts for future delivery of an underlying asset. The asset can be a physical commodity (corn, oil, precious metals, and so on) or financial instruments (bonds, currencies, stocks indices, and so on). Commodities differ from most financial assets in that they are continuously produced and consumed. The no-arbitrage based models of commodities dominate the current literature and practice on energy derivatives. These models are based on mean reverting stochastic processes which give as a result affine models such as Schwartz (1997) or Nielsen and Schwartz (2004). These models are particular attractive from practitioner’s perspective since they provide closed-form solutions to evaluate futures and some other derivatives contracts. This in turn allows for a relatively easy calibration and computational implementation. In these models, however, the drift and the volatility of the stochastic processes are usually specified as simple parametric functions for pure simplicity and tractability and it is not clear that these stochastic processes are the best in order to explain the behaviour of the spot prices and the convenience yields. In this paper, we derive some exact results which relate the risk-neutral drifts to the slope of the commodities futures price jointly with the factors. This fact allows us to estimate some of the coefficients of the pricing partial differential equation directly from the futures data available in the markets. Moreover, we do not have to estimate either the physical drift or the market price of risk. Therefore we considerably reduce the number of functions to estimate and, as a consequence, we reduce the computational cost as well as the misspecification error. Analogous results, although for a term structure model, are showed in Gómez-Valle and Martínez-Rodríguez (2008). In order to investigate the finite sample properties of this approach we carry out some numerical experiments. Finally, an application to crude oil and natural gas futures contracts traded at the New York Mercantile Exchange (NYMEX) is also illustrated.
منابع مشابه
Pricing of Commodity Futures Contract by Using of Spot Price Jump-Diffusion Process
Futures contract is one of the most important derivatives that is used in financial markets in all over the world to buy or sell an asset or commodity in the future. Pricing of this tool depends on expected price of asset or commodity at the maturity date. According to this, theoretical futures pricing models try to find this expected price in order to use in the futures contract. So in this ar...
متن کاملPricing of Futures Contracts by Considering Stochastic Exponential Jump Domain of Spot Price
Derivatives are alternative financial instruments which extend traders opportunities to achieve some financial goals. They are risk management instruments that are related to a data in the future, and also they react to uncertain prices. Study on pricing futures can provide useful tools to understand the stochastic behavior of prices to manage the risk of price volatility. Thus, this study eval...
متن کاملEmpirical Performance of Alternative Option Pricing Models for Commodity Futures Options
The central part of pricing agricultural commodity futures options is to find appropriate stochastic process of the underlying assets. The Black’s (1976) futures option pricing model laid the foundation for a new era of futures option valuation theory. The geometric Brownian motion assumption girding the Black’s model, however, has been regarded as unrealistic in numerous empirical studies. Opt...
متن کاملOption Pricing on Commodity Prices Using Jump Diffusion Models
In this paper, we aim at developing a model for option pricing to reduce the risks associated with Ethiopian commodity prices fluctuations. We used the daily closed Unwashed Lekempti grade 5 (ULK5) coffee and Whitish Wollega Sesame Seed Grade3 (WWSS3) prices obtained from Ethiopia commodity exchange (ECX) market to analyse the prices fluctuations.The natures of log-returns of the prices exhibit a...
متن کاملValuing Real Options using Implied Binomial Trees
A real option on a commodity is valued using an implied binomial tree (IBT) calibrated using commodity futures options prices. Estimating an IBT in the absence of spot options (the norm for commodities) allows real option models to be calibrated for the first time to market-implied probability distributions for commodity prices. Also, the existence of long-dated futures options means that good ...
متن کاملذخیره در منابع من
با ذخیره ی این منبع در منابع من، دسترسی به آن را برای استفاده های بعدی آسان تر کنید
برای دانلود متن کامل این مقاله و بیش از 32 میلیون مقاله دیگر ابتدا ثبت نام کنید
ثبت ناماگر عضو سایت هستید لطفا وارد حساب کاربری خود شوید
ورودعنوان ژورنال:
- Mathematical and Computer Modelling
دوره 57 شماره
صفحات -
تاریخ انتشار 2013