Advanced Commodity Trading Techniques by J.D. Hamon

By J.D. Hamon

Famous technical analyst J.D. Hamon unearths validated recommendations and strong new concepts which turn out you could win substantial in commodities.

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E. 2) is valid for Z under P. We find Iterating this we get the martingale property. However, it is generally no longer true that the increments of the new martingales Z(1), ... ,z{n) conditional on F t are orthogonal. To be more precise, the new basis martingales under P do not have the following two properties that the original basis martingales have under the physical measure: Firstly, the increments of the new basis martingales have a conditional variance different from one. e. 3) is no longer valid.

M < n) there remain degrees of freedom for the market prices of risk. To eliminate these would require additional information such as additional price processes not carrying new sources of risk. g. Cox, Ingersoll, and Ross [11]). 12) corresponds to a certain risk-neutral measure and vice versa. 6 A negative market price of risk can be intuitive from an economic point of view when we for instance think of a risk-loving representative investor in an equilibrium setup. 4 Normalized Price Processes 35 Finally, changing the measure to derive the dynamics of the assets using the drift restriction, we end up with the drift equal to the risk-free rate under the corresponding risk-neutral measure.

4 Using this result, we are able to derive the dynamics of the stochastic processes under the new measure. 3 4 These can again be found in Musiela [33]. g. Baxter [4]). 2 (Dynamics Under the New Measure). 1, are where j = 1, .. ,n. 8) We see that the dynamics of the stochastic processes under any two equivalent measures only differ with respect to the drift term, whereas the covariance structure remains the same, since the covariance structure of the new Brownian motion has not changed. This result holds for any stochastic process, no matter if it represents a basis asset or a state variable.

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