Special Session 118: Recent advances in mathematical finance

No-arbitrage perturbations of implied volatility

Michael Tehranchi
University of Cambridge
England
Co-Author(s):    
Abstract:
Possible shapes of the implied volatility smile are constrained by the absence of static arbitrage. For the sake of generating stress-testing scenarios, it is useful to consider prices after a perturbation of an observed implied volatility smile. However, some perturbations (for example, parallel shifts and scalings) do not respect the no-arbitrage constraints. A family of admissible perturbations is proposed.