A Tale in Three Cities : Comparison between GVV, SVI and IRV (Presentation Slides)

This presentation was based on the work of Jian Sun and Qiankun Niu, and presented at Morgan Stanley Global Modeling Meeting by Qiankun Niu on August 27, 2014. We thank Peter Carr for his invitation.Market Model is classified as the approach to model the implied volatility surface directly, which based on the observation that vallina options are liquidity traded in the market and the prices are driven by supply and demand factors. No-arbitrage imposes strict and complicated shape constraints on the implied volatility surface. Existed solution for this issue is to use another assistant quantity but sacrifice the simplicity of market models. To the best of our knowledge, a full arbitrage-free market model for the evolution of the implied volatility surface has yet to be developed.This work is an extension of the recent paper Carr and Sun (2013). The main thrust of this paper is to first follow the market model approach to establish a no arbitrage model named IRV model with simple closed form formula. Then, we will demonstrate the consistency between our IRV model and other two empirical models: SVI model in Gatheral and Jacquier (2014) and GVV model in Arslan et al. (2009). Potential application will be discussed in later sections. Applying the new model to the S&P 500 index options market and swaption market, the calibration results show that the model proposed in this paper works very well