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TheCorpFinanceQuant
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### Random Walk - Market Invariants

Reading through Atillio Meucci's questions for his Risk and Asset Allocation book. One of the questions

Q3.1.1 - Generate a Merton jump-diffusion process Xat discrete times with arbitrary parameters. What are the invariants in this process?

Any ideas on what these invariants would be?

Alan
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### Re: Random Walk - Market Invariants

A brief google suggests his "invariants" just mean (a set of) IID variates. In that model, as in every exponential Levy process, the log-returns over (disjoint) fixed intervals are IID variates. So the answer is likely any set: $\{\log P(t_i)/P(t_{i-j})\}$, with $P(t_i)$ the model prices, and $j$ some fixed integer. (Again, non-overlapping entries). The terminology seems idiosyncratic. I avoided using your $X_t$ because I don't know if those are prices or log-prices.