Abstract
This paper considers the pricing of European options on assets that follow a stochastic differential equation with a quadratic volatility term. We correct several errors in the existing literature, extend the pricing formulas to arbitrary root configurations, and list alternative representations of option pricing formulas to improve computational performance. Our exposition is based entirely on probabilistic arguments, adding a fresh perspective and new intuition to the existing PDE-dominated literature on the subject. Our main tools are martingale methods and shifts of probability measures; the fact that the underlying process is typically a strict local martingale is carefully considered throughout the paper.
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Andersen, L. Option pricing with quadratic volatility: a revisit. Finance Stoch 15, 191–219 (2011). https://doi.org/10.1007/s00780-010-0142-8
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DOI: https://doi.org/10.1007/s00780-010-0142-8
Keywords
- Quadratic volatility
- Strict local martingale
- Put and call option pricing
- Hitting time densities
- Fourier series
- Method of images