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Option pricing and hedging models with analytical formulas, implied volatility smile calibration (SABR & Displaced-Diffusion), exotic payoff replication, and dynamic hedging.

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rohen97/Stochastic-Modelling-Project

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Part 1 - Analytical Option Formulae

Formulas for European Payoffs for (i) Vanilla Calls & Puts ; (ii) Cash-or-Nothing Calls & Puts ; (iii) Asset-or-Nothing Calls & Puts

Stock Price Process Models: 1) Black-Schloes ; 2) Bachelier ; 3) Black76 ; 4) Displaced-Diffusion

Part 2 - Model Calibration

Plotting of Implied Volaitlity Smile (IV against K for Out-of-Money and At-the-Money options) SABR Model and Displaced-Diffusion Model

Part 3 - Pricing of Exotic European payoff using Static Replication

Part 4 - Dynamic Hedging

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Option pricing and hedging models with analytical formulas, implied volatility smile calibration (SABR & Displaced-Diffusion), exotic payoff replication, and dynamic hedging.

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