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What is the expectation of W multiplied by the exponential of W?

Using the moment-generating function of a standard normal distribution.

Data Exploration

Basic applications with numpy and pandas.

What is the probability of returning to the starting vertex after n steps?

Using the conditional probability with respect to the previous step.

How to price an Option under the Black-Scholes model?

Deriving European option pricing formulas under a lognormal model.

How to Price an Option under the Bachelier Model?

Deriving European option pricing formulas under a normal model.