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CM2: Financial Engineering & Loss Reserving
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Module 5
Stochastic Processes for Asset Prices
1
Modeling Asset Prices with Geometric Brownian Motion (GBM)
Write the Stochastic Differential Equation (SDE) for geometric Brownian motion (GBM) to model asset prices.
2
Applying Itô's Lemma to Stock Price Processes
Apply Itô's lemma to functions of a stock price process, including deriving the SDE for log(S_t).
3
Deriving Lognormal Stock Prices from GBM
Solve the SDE for GBM to derive the lognormal stock price distribution.
4
Estimating Lognormal Model Parameters from Historical Prices
Estimate the drift and volatility parameters of the lognormal model from historical price data.
5
Lognormal Stock Price Model: Probabilities and Quantiles
Calculate probabilities and quantiles of future stock prices under the lognormal model.
6
Limitations of the Continuous-Time Lognormal Model
Describe the primary limitations of the continuous-time lognormal model.
7
The Wilkie Stochastic Investment Model: Structure & Application
Describe the structure and application of the Wilkie stochastic investment model.
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Asset Pricing Models
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Fundamentals of Derivative Securities