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|Title:||Option volatility and the acceleration Lagrangian|
|Authors:||Baaquie, B.E. |
|Keywords:||Lagrangian with acceleration|
|Citation:||Baaquie, B.E., Cao, Y. (2014-01-01). Option volatility and the acceleration Lagrangian. Physica A: Statistical Mechanics and its Applications 393 : 337-363. ScholarBank@NUS Repository. https://doi.org/10.1016/j.physa.2013.07.074|
|Abstract:||This paper develops a volatility formula for option on an asset from an acceleration Lagrangian model and the formula is calibrated with market data. The Black-Scholes model is a simpler case that has a velocity dependent Lagrangian. The acceleration Lagrangian is defined, and the classical solution of the system in Euclidean time is solved by choosing proper boundary conditions. The conditional probability distribution of final position given the initial position is obtained from the transition amplitude. The volatility is the standard deviation of the conditional probability distribution. Using the conditional probability and the path integral method, the martingale condition is applied, and one of the parameters in the Lagrangian is fixed. The call option price is obtained using the conditional probability and the path integral method. © 2013 Elsevier B.V. All rights reserved.|
|Source Title:||Physica A: Statistical Mechanics and its Applications|
|Appears in Collections:||Staff Publications|
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