A good model balances (capturing market features) with tractability (solvable via mathematics or computation).
Because most advanced financial models lack closed-form solutions , computational methods are required to approximate results: Mathematical Modeling - Computation in Finance mathematical modeling and computation in finance pdf
𝜕V𝜕t+12σ2S2𝜕2V𝜕S2+rS𝜕V𝜕S−rV=0the fraction with numerator partial cap V and denominator partial t end-fraction plus one-half sigma squared cap S squared the fraction with numerator partial squared cap V and denominator partial cap S squared end-fraction plus r cap S the fraction with numerator partial cap V and denominator partial cap S end-fraction minus r cap V equals 0 is the option price. is the underlying stock price. is the asset volatility. is the risk-free interest rate. 2. Local and Stochastic Volatility Models A good model balances (capturing market features) with