This paper proposes a Brownian time change for modeling stochastic volatility and combines it with a drifted variance gamma process in deriving explicit pricing methods for exotic power options in the presence of jumps and volatility clustering. In view of the changeful payoff structure of exotic options, the underlying stock is assumed to pay constant dividends on a continuous basis. In-depth analysis of properties of the time change as well as the time-changed process is focused on characteristic functions, which facilitate pricing via Fourier transform. The pricing mechanism of plain-vanilla options is discussed as a basis for pricing power options. Also, Monte-Carlo simulation techniques are studied through time discretization while empirical analysis is conducted on real financial markets. My objective is to study the theoretical elements of this stochastic-volatility model and its interesting advantages in the context of power option pricing.
Mathematics Subject Classication: 60E10; 60G51; 91G20
Keywords: Brownian time change; Variance gamma process; Power options; Characteristic function