خلاصة:
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 article, three futures pricing models have been considered. In the first model, one-factor pricing model without spot price jump has been presented. In this model futures price of commodity is a function of spot price and remaining time to maturity. In the others, the models have been expanded by using jump-diffusion processes and stochastic jump in spot price. Then, to empirically study the models, NYMEX WTI crude oil futures price data has been used and parameters have been estimated with Kalman filter algorithm. The empirical results show that the one factor model with uniform jump is suitable to explain the crude oil spot price behavior and its futures price. This model and estimated parameters provide the useful tool to predict NYMEX WTI oil future prices.
ملخص الجهاز:
"By using jump-diffusion Ito's lemma for (6) it can be written: by using , it is obtained as no-jump model: (View the image of this page) (7) (8) Using the previous equation that shows the dynamics of spot price in equivalent probability space, the closed answer of futures price / is obtained by using Daffie-Pan-Singleton approach and application of Affine functions.
(View the image of this page) figure (1) – Filtered state variable (oil spot price) ( ) and the one month oil futures price (F1) / one factor pricing model without jump Source: The research findings Table (1) shows the parameters of one factor futures pricing model with jump by assuming that spot price follows the process of jump-diffusion with stochastic exponential jump amplitude.
According to the specified model and using of Kalman filter algorithm into the importance state space model, the oil mean rate of return (μ), the oil rate of return volatility (σ), the market value of risk respect to one unit of spot price (M), the rate of spot price jump number (η), the upper bound of jump amplitude (U) depends on the uniform distribution of jump size and the lower bound of jump amplitude (D) related to the uniform distribution of jump in the model were estimated.
figure (3) – Filtered state variable (oil spot price) (/) and the one month oil futures price (F1) / one factor pricing model with uniform jump Source: The research findings All three parameters of jump part, include rate of spot p(View the image of this page)rice jump number (η), the upper bound of jump amplitude (U) and the lower bound of jump amplitude (D) are statistically significant in this model."
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