Black-Scholes Algorithmic Delta Hedging

Maintaining a Risk-Free Portfolio with European Options

Financial Derivatives

Financial derivatives allow the opportunity to speculate and hedge an underlying asset. Options are one of those instruments, commonly used to hedge portfolio exposure. There are different types of options European: exercise at expiry, American: exercise throughout life of option, Bermudan: exercise at set dates throughout life of option; in this case we will be analyzing European options. The effectiveness of the hedge is decided by the model assumptions and method used to price the derivative, and the frequency of portfolio rebalancing to maintain the hedge. If one were to use a single step binomial tree to calculate a delta for an option contract, establish a portfolio based on that delta, and update the portfolio with respect to that delta every month to maintain a risk free portfolio (a hedged portfolio) the outcome would be very different from an individual who uses the Black-Scholes model to calculate a delta every tick and update the portfolio with respect to the delta every tick to maintain a risk free portfolio. This is where algorithmic hedging comes into play, by using similar principles from algorithmic trading, we can establish and maintain an effective risk free portfolio until we have the right to exercise…