Volatility Surface Calibration In Illiquid Market Environment

In this paper, we show the fragility of widely-used Stochastic Volatility Inspired (SVI) methodology. Especially, we highlight the sensitivity of SVI to the fitting penalty function. We compare different weight functions and propose to use a novel methodology, the implied vega weights. Moreover, we unveil the relationship between vega weights and the minimization task of observed and fitted price differences. Besides, we show that implied vega weights can stabilize SVI surfaces in illiquid market conditions. INTRODUCTION Vanilla options are traded with finite number of strikes and maturities. Thus, we can observe only some points of the implied volatility surface. It is known that vanilla prices are arbitrage free hence exotic option traders would like to calibrate their prices to vanillas (Dupire 1994). The main difficulty is that calibration methods need the implied volatility surface. To overcome this problem we have to construct an arbitrage free surface from the observed points (Schönbucher 1998, Gatheral 2013). In this paper we provide a robust arbitrage free surface fitting methodology. Chapters are structured as follows: Section 2. is a brief overview of SVI. In Section 3. we compare the different weight functions and present our implied vega weight L methodology. In Section 4. we summarize the findings.