Why are quadratic normal volatility models analytically tractable?
We discuss the class of "Quadratic Normal Volatility" models, which have drawn much attention in the financial industry due to their analytic tractability and flexibility. We characterize these models as the ones that can be obtained from stopped Brownian motion by a simple transformation and a change of measure that only depends on the terminal value of the stopped Brownian motion. This explains the existence of explicit analytic formulas for option prices within Quadratic Normal Volatility models in the academic literature.
|Date of creation:||Feb 2012|
|Date of revision:||Mar 2013|
|Publication status:||Published in SIAM Journal on Financial Mathematics, 2013 4:1, 185-202|
|Contact details of provider:|| Web page: http://arxiv.org/|
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- Peter Carr & Katrina Ellis & Vishal Gupta, 1998. "Static Hedging of Exotic Options," Journal of Finance, American Finance Association, vol. 53(3), pages 1165-1190, 06.
- Rady, Sven, 1994. "The Direct Approach to Debt Option Pricing," Munich Reprints in Economics 3404, University of Munich, Department of Economics.
- Miltersen, Kristian R & Sandmann, Klaus & Sondermann, Dieter, 1997.
" Closed Form Solutions for Term Structure Derivatives with Log-Normal Interest Rates,"
Journal of Finance,
American Finance Association, vol. 52(1), pages 409-430, March.
- Miltersen, K. & K. Sandmann & D. Sondermann, 1994. "Closed Form Solutions for Term Structure Derivatives with Log-Normal Interest Rates," Discussion Paper Serie B 308, University of Bonn, Germany.
- K. Sandmann & Sandmann, K., 1995. "The Direct Approach to Debt Option Pricing," Discussion Paper Serie B 212, University of Bonn, Germany.
- Sven Rady, 1997. "Option pricing in the presence of natural boundaries and a quadratic diffusion term (*)," Finance and Stochastics, Springer, vol. 1(4), pages 331-344.
- Peter Carr & Travis Fisher & Johannes Ruf, 2012. "On the Hedging of Options On Exploding Exchange Rates," Papers 1202.6188, arXiv.org, revised Nov 2013. Full references (including those not matched with items on IDEAS)
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