Option Pricing and Stochastic Calculus

We show how options can be priced in the Black and Scholes framework, from a probabilistic point of view and from a simpler hedging argument. We derive the formulae for the price and basic sensitivities: delta, gamma, vega and theta. We also show how more exotic instruments such as digitals and barriers can be priced.

Introduction to Derivatives, Black and Scholes Assumptions.

Derivation of Option Price formulae using PDE approach

Derivation of Option Price formulae using Martingale approach

Option Greeks – Delta, Gamma, Vega and Theta.

P&L analysis – Hedging cost equals cost of option

Pricing Digital Options

Barrier Options, Reflection Pricinciple and Girsanov Theorem

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