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CM2: Financial Engineering & Loss Reserving
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Module 8
The Black-Scholes-Merton Model
1
Assumptions of the Black-Scholes-Merton Model
State the assumptions of the Black-Scholes-Merton (BSM) model.
2
Deriving the Black-Scholes-Merton PDE
Explain the logic of deriving the BSM PDE using a continuously rebalanced, delta-hedged portfolio.
Black-Scholes Model: Pricing European Options
Apply the Black-Scholes formula to calculate European call and put prices.
4
Black-Scholes-Merton Model with Continuous Dividends
Adjust the BSM formula for stocks paying continuous dividends.
5
Calculating Implied Volatility from Option Prices
Explain how to find the implied volatility from an observed market option price.
6
BSM Model Limitations & the Volatility Smile
Describe key limitations of the BSM model, such as the volatility smile.
7
Market Completeness and Martingale Representation in Derivative Pricing
Explain how market completeness and the martingale representation theorem support derivative pricing.
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Risk-Neutral Pricing in Discrete Time
Next module
Option Price Sensitivities: The Greeks