F# for Quantitative Finance

Delta hedging using Black-Scholes

A delta neutral portfolio is constructed by an option and the underlying instrument. The portfolio will, in theory, be immune against small changes in the underlying price. When talking about delta hedging, the hedge ratio of a derivative is used to define the amount of underlying price needed for each option. Delta hedging is the trading strategy that maintains a delta neutral portfolio for small changes in the underlying price.

Briefly, let's look at how to do this in practice. Suppose we have N derivatives. This needs to be hedged to protect against price movements. We then need to buy the underlying stock to create the hedge. The whole procedure can be described in three steps:

1. N derivatives need to be delta ...