Mathematical Principles and Quantitative Finance · 19. avril 2024
The trigonometric circle extends complex numbers, useful for visualizing periodic phenomena. In option pricing, the binomial model reflects market uncertainty through a tree structure. Fourier transforms help analyze future payoffs, using the characteristic function of the underlying asset's distribution. Circular convolutions connect binomial models and Fourier transforms, facilitating efficient computation of option prices.
13. novembre 2023
Discretization translates continuous financial models into numerically solvable steps, crucial for derivative pricing and risk management. It simplifies complex models, enabling simulations like Monte Carlo for exotic options while introducing some approximation error. #QuantitativeFinance #DerivativesPricing #NumericalMethods
05. novembre 2023
Put-Call Symmetry (PCS) links European put and call option prices via the forward price of the underlying asset. It requires frictionless markets, no arbitrage, zero drift, and symmetric asset returns. PCS is practical for pricing and hedging exotic options, offering a simpler alternative to dynamic hedging by balancing put and call strike prices against the forward price.