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Protter [36]), but for certain problems it might be more appropriate to look at a discrete setting, being a better approximation of reality. Furthermore, for complex problems it may be more adequate to start in discrete time, avoiding tedious technical conditions necessary in continuous time. In this context, the question arises whether all properties of the diffusion setup carryover to the discrete scenario. We will see that this is not always the case. On the one hand, it is shown that the key results and the economic intuition are similar in the continuous and discrete setting: We can formulate the dynamics of the stochastic processes in the discrete model in the same fashion as in the continuous model.

4 Normalized Price Processes As we have seen in Chap. 2, numeraires play an important role in martingale pricing. The relevant numeraires in the derivation of the BS formula are the MMA and the underlying asset. Besides these, we take a look at an arbitrary positive portfolio as the numeraire consisting of a linear combination of the basis assets. This is of interest with regard to the power option in Chap. 4. 2 within both the diffusion and the discrete setup. Then, we calculate the dynamics of the assets under the new measure, which is necessary for the explicit computation of the artificial probabilities as discussed in Chap.

We assume that the Brownian motion generates the filtration. The dynamics of the adapted stochastic processes SCi), i = 1, ... g. Protter [36]). Recall that we only consider processes adapted to the filtration generated by the Brownian motion. For the asset S(i), i = 1, ... , m, the drift J-Li i ) can be interpreted as the expected return of the asset over an infinitesimal time interval [t, t + dtJ. The dynamics of the MMA are given by dBt = rtBt dt , with a deterministic interest rate rt and Bo = 1 so that B t = exp (1 rsds).

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Pattern Recognition, Price And The RSI by Knaggs J.

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