Option pricing in a sentiment-biased stochastic volatility model

This paper presents a Markov-modulated stochastic volatility model that captures the dependency of market regimes on investor sentiment. The main contribution lies in developing a modified version of the classical Heston model by allowing for a sentiment-driven bias in the volatility of the asset. Specifically, a two-factor Markov-modulated stochastic volatility model is proposed, integrating a diffusion coefficient in the risky asset dynamics and a correlation parameter influenced by both the volatility process and a continuous-time Markov chain accounting for the sentiment-bias. Diverging from conventional approaches in option pricing models, this framework operates under the real-world probability measure, necessitating considerations about the existence of an equivalent martingale pricing measure. The purpose of this paper is to derive a closed formula for the pricing of European-style derivatives and to fit the model on market data through a suitable calibration procedure. A comparison with the Heston benchmark model is provided for a sample of Apple, Amazon, and Bank of America stock options.