WIT Press

Path Dependent Options: The Case Of High Water Mark Provision For Hedge Funds


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Z. Li & S. S.-T. Yau


High Water Mark (HWM) provision is an important feature in the hedge fund industry. The framework of the option pricing with HWM provision for hedge funds is developed in this paper. The closed forms of HWM look-back put option, Russian option and stop-loss option are derived. We also obtain the internal relationship between HWM look-back put and the traditional look-back option. We show that HWM look-back put is cheaper than the traditional look-back put, and the higher the incentive fee, the lower the option price. Keywords: high water mark options, stochastic processes, hedging. 1 Introduction Hedge funds are pooled investment vehicles;most set up as private limited partnerships and investors buy an interest into the partnership. As such, they have more freedom and flexibility than mutual funds. In the past ten years, the number of hedge funds has risen about 20% per year. Currently, there are estimated to be 4000-5000 hedge funds managing $200-$300 billion. While the number and size of hedge funds are small relative to mutual funds, their growth reflects the importance of this alternative investment category. One important feature of the hedge funds industry is the structure of the fee paid to fund managers. The fee in a hedge fund’s account mainly comprisesmanagement fee and incentive fee. Management fee is charged on the account balance whether the account is profitable or not. Management fee normally ranges between 1%-2.5% annually,


high water mark options, stochastic processes, hedging.