Volatility curve generation using the Heston Model

Abstract

The objective of the paper is to generate a volatility curve for the USDINR currency pair based on the Heston model. For any tenor, I will be using the ATM implied volatility, the 25 Delta Risk Reversal implied volatility, and the 25 Delta Butterfly implied volatility as inputs. I intend to use MATLAB as the programming tool. The aim is to compare the generated volatility curve with the observed market volatility curve and consequently examine the efficacy of the Heston model.The paper will be confined to the USDINR currency market and the stochastic Heston model for the purposes of volatility curve generation. This working paper is structured as follows. We first introduce the FX variant of the Black Scholes model and typical quoting conventions in the FX options market. We then illustrate the Heston model and the methodology of the calibration process. We then summarize the results obtained from the calibration and analyze the success of the Heston model in replicating the actual implied volatility curve observed in the USDINR market. MATLAB was used for simulating the pricing and calibration routines demonstrated in this paper; the relevant code is presented in the appendix.