How to Hedge a Portfolio with Put Options

There are 2 good reasons to buy put options: because you think they are cheap because you want downside protection. In the latter case, you are looking to use the skewed payoff profile of the put option to protect a portfolio against large downside moves without capping your upside too much. The first requires a …

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Efficiently Simulating Geometric Brownian Motion in R

For simulating stock prices, Geometric Brownian Motion (GBM) is the de-facto go-to model. It has some nice properties which are generally consistent with stock prices, such as being log-normally distributed (and hence bounded to the downside by zero), and that expected returns don’t depend on the magnitude of price. Of course, GBM is just a …

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