Kou Jump-Diffusion Model
An extension of the Black-Scholes framework incorporating sudden, large discontinuities in asset prices via a double-exponential jump process. The project consists of two modules.
The first is a pricing and calibration engine for European options, combining the Carr-Madan FFT method with 2D interpolation for efficient price computation, and L-BFGS-B optimization to fit model parameters to market data.
The second is a Monte Carlo simulation analyzing delta-hedging performance under jump risk. By evolving a hedged European call option portfolio under the Kou model, the simulation demonstrates that jumps induce fat tails in the P&L distribution that delta-hedging alone cannot eliminate.