Abstract
In my paper I focus on the growth of knowledge in finance from an heuristic viewpoint and I propose the analysis of two different knowledge-advancing strategies usually adopted at the frontier of knowledge, i.e. problem-solving and model-building. I show how these two strategies, even though both effective in the short-run, nonetheless provide descriptions of the target object and which are different in their descriptive and knowledge-advancing depth. In order to do so, I propose a case study borrowed from the modelling activities in the Libor market.
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Notes
In her analysis of models' evolution from general concepts to tools, she detects two possible labels to distinguish the actions of models within economic theories and with respect to economic objects. On the one side, she argues that models as "investigating" and reasoning tools aid economists in using and applying their knowledge to specific context problems. On the other hand, models as "manipulating" devices show their potential in terms of creative tools, enabling inquirers in manipulating objects and creating knowledge. In the context of this paper, it could be then argued that in the first case models would work as epistemic objects, thus providing better explanations of already measured phenomena or better descriptions for already known objects. On the contrary, in the second case they would work as heuristic objects, thus enabling for the expansion of theories towards "unknown territories".
In Preda (2009), p. 41.
The equation is determined by the following conditions: \(f\left( {0, t} \right)\) describing the current forward rate curve; \(\alpha (t,T)\) describing the drift of the forward rate curve; \(W^{Q}\) describing the vector of the Wiener process; \(\sigma \left( {t, T} \right)\) describing the volatility structure.
Markov property applies to discrete processes in which in every determined instant \(t_{n + 1}\) the probability of a state \(E_{j}^{n + 1}\) depends exclusively on \(t_{n + 1}\) and \(E_{i}\) at instant \(t_{n}\). In other words: the actual state of the system summarises every useful information to know its future behaviour, since the evolution of a markovian stochastic process depends only on the actual value of its state variable. In a non- markovian stochastic process, on the other hand, the probability distribution of a given state is inherently path- dependent, and this means that it is also affected by information about the past state of its variables.
This is how a so called "bushy", non- recombining tree diagram looks like:
and its "messy" structure is useful in continuous- time model. On the other hand, this is how a recombining lattice diagram, used in discrete- time model, looks like:
.This model is also known as "Brace-Gatarek-Musiela" (BGM) Model, with reference to its main inventors.
and its "messy" structure is useful in continuous- time model. On the other hand, this is how a recombining lattice diagram, used in discrete- time model, looks like:
.References
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Miotti, G. Model Building and Problem Solving: A Case from Libor Market Derivatives. Topoi 40, 783–791 (2021). https://doi.org/10.1007/s11245-019-09652-7
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DOI: https://doi.org/10.1007/s11245-019-09652-7