Riskless Hedge Approach

The riskless hedge approach involves constructing a portfolio that eliminates the risk associated with the underlying asset, resulting in a riskless investment. In the context of the Binomial Option Pricing Model, this approach involves creating a portfolio of the option and a certain number of shares of the underlying asset.

European Call and Put Options: For European options, the riskless hedge approach requires continuously adjusting the portfolio’s composition to maintain a riskless position. The number of shares of the underlying asset is determined by the option’s delta, which represents the sensitivity of the option price to changes in the underlying asset’s price. By balancing the option position with the shares, a riskless hedge is achieved, ensuring a constant portfolio value regardless of the underlying asset’s price movements.
American Call and Put Options: The riskless hedge approach can be extended to American options as well. In the binomial model, at each node of the option price tree, the portfolio is adjusted by buying or selling additional shares to maintain a riskless hedge. The optimal exercise strategy is determined by comparing the value of exercising the option immediately with the value of holding the option and the hedged portfolio until the next time step. This allows for evaluating early exercise opportunities and determining the option’s value