High-water Standard Under The Terms Of The Hedge Fund Option Pricing

As the rapid growth of hedge fund industry, more and more products are also being developed to provide access to underlying hedge funds, and options on hedge fund are regarded to be the most fascinating one. Because incentive fees for money managers are frequently accompanied by high water mark (for short, HWM) provisions, one natural question for options on hedge funds is how significant this HWM provision impacts on option pricing.In this thesis, we first work in a continuous-time framework and assume that the fund NAV follows a lognormal diffusion process, then we develop the framework of the option pricing with HWM provision for hedge funds. The closed forms of HWM look-back put option are derived with constant volatility. We show that HWM look-back put is cheaper than the traditional look-back put, and investigate the effect of incentive fee and initial value of NAV/HWM.However, the real world return distributions for many of the hedge fund strategies display both skewness and kurtosis. To deal with this problem, we introduce stochastic volatility (for short, SV) model which corrects the simple lognormal normal distribution and constant volatility assumption. We implement Heston's SV model using Monte Carlo simulation, and investigate the effects of the model parameters by looking at the pricing results. Especially, we show that correlation between volatility and fund NAV is necessary to generate skewness. However, stochastic volatility only changes the kurtosis without this correlation.