Abstract:
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 evaluates commodity futures contracts by considering Ross (1995) one-factor future pricing model as a function of spot price, Gibson and Schwartz (1990) two-factor futures pricing model as a function of spot price and convenience yield and finally Schwartz (1997) three-factor futures pricing model as a function of spot price, convenience yield and instantaneous interest rate by adding jump to stochastic behavior of commodity spot price. For this purpose, it is assumed that spot price follows Jump-diffusion stochastic process with exponential probability distribution of jump domain. Finally, commodity pricing future relations in three basic models are presented as a function of above factor(s) and jump parameters by using Duffy-Pan- Singleton approach.
Machine summary:
Pricing of Futures Contracts by Considering Stochastic Exponential Jump Domain of Spot Price Hossein Esmaeili Razi1 PhD in Economics, University of Isfahan, Isfahan, Iran Rahim Dallali Esfahani Department of Economics, University of Isfahan, Iran Abstract Derivatives are alternative financial instruments which extend traders opportunities to achieve somefinancial goals.
Finally, commodity pricing future relations in three basic models are presented as a function of above factor(s) and jump parameters by using Duffy-Pan- Singleton approach.
In this study, the theoretical pricing of commodity futures contract is considered as three models of one-factor, two-factor and three- factor pricing that are presented by using Exponential probability distribution of jump domain in underlying commodity spot price.
Therefore, they add separately short-term and long-term jumps on stochastic behavior of spot price in Schwartz and Smith (2000) model to extract commodity futures price relations.
Martin value of the domain of spot price stochastic reduction jump is shown by that follows the exponential probability distribution with rate parameter γ .
In this section, Ross and Schwartz one-factor futures pricing model is developed by adding Based on this relationship, logarithm of spot price will follow Mean Reversion jump-diffusion Process where represents the mean of log spot price, κ > 0 is speed of adjustment, σ is the standard deviation from the mean value and is Standard Brownian Process.
(1991), Contingent Claims Evaluation When the Convenience Yield Is 2 2 3 2 ( ))] Stochastic: Analytical Results, Working − ( + ) (1 − −(+) − Commodity futures price show in Equation (47) is the same as three-factor model pricing of Schwartz (1997), but jump term make some changes.