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When the underlying stock price is a strict local martingale process under an equivalent local martingale measure, Black-Scholes PDE associated with an European option may have multiple solutions. In this paper, we study an approximation for the smallest hedging price of such an European option. Our results show that a class of rebate barrier options can be used for this approximation. Among of them, a specific rebate option is also provided with a continuous rebate function, which corresponds to the unique classical solution of the associated parabolic PDE. Such a construction makes existing numerical PDE techniques applicable for its computation. An asymptotic convergence rate is also studied when the knocked-out barrier moves to infinity under suitable conditions.
Trading option strangles is a highly popular strategy often used by market participants to mitigate volatility risks in their portfolios. In this paper we propose a measure of the relative value of a delta-Symmetric Strangle and compute it under the
Most trading in cryptocurrency options is on inverse products, so called because the contract size is denominated in US dollars and they are margined and settled in crypto, typically bitcoin or ether. Their popularity stems from allowing professional
We introduce a new class of processes for the evaluation of multivariate equity derivatives. The proposed setting is well suited for the application of the standard copula function theory to processes, rather than variables, and easily enables to enf
These notes are the first half of the contents of the course given by the second author at the Bachelier Seminar (February 8-15-22 2008) at IHP. They also correspond to topics studied by the first author for her Ph.D.thesis.
A nonlinear wave alternative for the standard Black-Scholes option-pricing model is presented. The adaptive-wave model, representing controlled Brownian behavior of financial markets, is formally defined by adaptive nonlinear Schrodinger (NLS) equati