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Register a new userModeling the commodity prices of base metals in Indian commodity market using a Higher Order Markovian Approach
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Siddhartha Chakrabarty
Publication date
2020
fields
Financial
and research's language is
English
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A Higher Order Markovian (HOM) model to capture the dynamics of commodity prices is proposed as an alternative to a Markovian model. In particular, the order of the former model, is taken to be the delay, in the response of the industry, to the market information. This is then empirically analyzed for the prices of Copper Mini and four other bases metals, namely Aluminum, Lead, Nickel and Zinc, in the Indian commodities market. In case of Copper Mini, the usage of the HOM approach consistently offer improvement, over the Markovian approach, in terms of the errors in forecasting. Similar trends were observed for the other base metals considered, with the exception of Aluminum, which can be attributed the volatility in the Asian market during the COVID-19 outbreak.
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We introduce an agent-based model, in which agents set their prices to maximize profit. At steady state the market self-organizes into three groups: excess producers, consumers and balanced agents, with prices determined by their own resource level and a couple of macroscopic parameters that emerge naturally from the analysis, akin to mean-field parameters in statistical mechanics. When resources are scarce prices rise sharply below a turning point that marks the disappearance of excess producers. To compare the model with real empirical data, we study the relations between commodity prices and stock-to-use ratios of a range of commodities such as agricultural products and metals. By introducing an elasticity parameter to mitigate noise and long-term changes in commodities data, we confirm the trend of rising prices, provide evidence for turning points, and indicate yield points for less essential commodities.
We design three continuous--time models in finite horizon of a commodity price, whose dynamics can be affected by the actions of a representative risk--neutral producer and a representative risk--neutral trader. Depending on the model, the producer can control the drift and/or the volatility of the price whereas the trader can at most affect the volatility. The producer can affect the volatility in two ways: either by randomizing her production rate or, as the trader, using other means such as spreading false information. Moreover, the producer contracts at time zero a fixed position in a European convex derivative with the trader. The trader can be price-taker, as in the first two models, or she can also affect the volatility of the commodity price, as in the third model. We solve all three models semi--explicitly and give closed--form expressions of the derivative price over a small time horizon, preventing arbitrage opportunities to arise. We find that when the trader is price-taker, the producer can always compensate the loss in expected production profit generated by an increase of volatility by a gain in the derivative position by driving the price at maturity to a suitable level. Finally, in case the trader is active, the model takes the form of a nonzero-sum linear-quadratic stochastic differential game and we find that when the production rate is already at its optimal stationary level, there is an amount of derivative position that makes both players better off when entering the game.
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