We investigate the distributions of epsilon-drawdowns and epsilon-drawups of the most liquid futures financial contracts of the world at time scales of 30 seconds. The epsilon-drawdowns (resp. epsilon- drawups) generalise the notion of runs of negative (resp. positive) returns so as to capture the risks to which invest…
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Fair valuation of Lévy-type drawdown-drawup contracts with general insured and penalty functionsq-fin.PR
The paper calculates fair premiums and optimal stopping rules for equity-linked contracts tied to drawdown and drawup events.
problem Fair valuation of equity-linked contracts tied to drawdown and drawup events.
method Fluctuation theory of Lévy processes and optimal stopping theory.
result Calculation of fair premiums and optimal stopping rules for equity-linked contracts.
Unified framework for drawdown risk computation under Markov models.
problem High computational challenges in drawdown risk metrics.
method Unified framework for computing five drawdown quantities under general Markov models, using linear systems and efficient algorithms.
result Efficient algorithms achieve same complexity as path-independent problems, validated by rigorous convergence analysis and extensive experiments.
Drawdown (resp. drawup) of a stochastic process, also referred as the reflected process at its supremum (resp. infimum), has wide applications in many areas including financial risk management, actuarial mathematics and statistics. In this paper, for general time-homogeneous Markov processes, we study the joint law of …