TY - JOUR
T1 - Implied Markov transition matrices under structural price models
AU - Defourny, Boris
AU - Moazeni, Somayeh
N1 - Publisher Copyright:
© 2021 The Author(s). Published by Informa UK Limited, trading as Taylor & Francis Group.
PY - 2021
Y1 - 2021
N2 - This paper proposes an approach to compute the implied transition matrices from observations of market data on financial derivatives, when the price of the underlying originates from a structural model and the payoffs are received over a period of time. The structural price model involves a price formation mechanism which computes the price based on a set of Markovian inputs and constrained optimization processes. The developed inference method relies on a linear description of the derivative values in terms of occupation measures of the payoff duration. We establish closed-form expressions between occupation measures and state transitions, which then enable us to characterize implied state transition probabilities consistent with the market data on the derivative values. We develop methods to solve the optimization problem with the resulting nonlinear occupation measure equation. Numerical illustrations of the approach are presented for financial derivatives on network capacities. By applying the method to an electric network, we investigate the relation between financial transmission correct contract values and a range of implied probabilities of congestion in the network.
AB - This paper proposes an approach to compute the implied transition matrices from observations of market data on financial derivatives, when the price of the underlying originates from a structural model and the payoffs are received over a period of time. The structural price model involves a price formation mechanism which computes the price based on a set of Markovian inputs and constrained optimization processes. The developed inference method relies on a linear description of the derivative values in terms of occupation measures of the payoff duration. We establish closed-form expressions between occupation measures and state transitions, which then enable us to characterize implied state transition probabilities consistent with the market data on the derivative values. We develop methods to solve the optimization problem with the resulting nonlinear occupation measure equation. Numerical illustrations of the approach are presented for financial derivatives on network capacities. By applying the method to an electric network, we investigate the relation between financial transmission correct contract values and a range of implied probabilities of congestion in the network.
KW - Energy derivatives
KW - Estimation of stochastic systems
KW - Markov processes
KW - Optimization
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U2 - 10.1080/14697688.2021.1921242
DO - 10.1080/14697688.2021.1921242
M3 - Article
AN - SCOPUS:85107923142
SN - 1469-7688
VL - 21
SP - 1935
EP - 1954
JO - Quantitative Finance
JF - Quantitative Finance
IS - 11
ER -