Trend Derivatives: Pricing, Hedging, and Application to Executive Stock Options

We introduce a new class of derivative products whose payoff is linked to the trend of the underlying instrument. Many institutional and private investors hold their investments for an extended period of time. The time of buying and selling is generally determined by multiple decision factors and not only by a pure investment analysis requiring an investment to be implemented at a specific point in time. Therefore, with limited flexibility in timing their investment decision, asset managers look for investments that would ideally be independent of the timing decision. Trend derivatives are complex path-dependent instruments whose payoffs are linked to the trend of a stock price or an index, making the timing of the decision less relevant. We show how trend derivatives are designed and priced. Due to their peculiar features, trend derivatives offer some interesting applications such as executive stock option plans.