The Pricing Formula for Exotic Options Based on a Discrete Investment Strategy

This paper proposes an option pricing model under a discrete investment strategy. From the perspective of investors’ initiative, we assume that the investor can take early actions before the underlying asset price reaches the strike level and trade a certain proportion of the underlying asset within the validity period of the option. Building on the Black–Scholes framework, we derive a closed-form pricing formula for options under the discrete investment strategy and compare the resulting prices with those obtained from the classical Black–Scholes model. Furthermore, after parameter calibration, our model exhibits smaller fitting errors when applied to market data. By incorporating investor agency into the pricing framework, this study further extends option pricing theory and offers theoretical insights into the prevention of financial risks.