Pricing Model Of Metal Futures Options Based On Fractal Market Theory And Its Empirical Study

Futures'price fluctuates sharply both at home and abroad, leading to an increasing demand for commodity risk management, which cannot be fulfilled by futures contracts. Commodity options play an important role in hedging risk in commodity corporations, completing futures market's functions and constructing commodity portfolio. The listing of commodity options is imperative for Chinese futures markets, especially in metal futures market. The core in study on futures options is valuation, and the price behavior process is the main factor that affects the validity of the pricing model. This paper consideres commodity futures market as a complex nonlinear dynamic system, and studies the futures options valuation on the basis of the nonlinear futures prices process, which is of both theoretic and realistic significance, especially for corporations'hedging market risk with options and completing futures market's functions.Firstly, this paper introduces the development of the global metal futures markets and the factors that affect the metal prices. Then, it decipts that futures market is a typical nonlinear dynamic system on the basis of fractal market theory. Next, it examines fractal features of copper and aluminum futures in Shanghai Futures Exchange (SHFE) and London Metal Exchange(LME) using R/S analysis method. The result shows that Hurst value is greater than 0.5 evidently indicating that there are overwhelming evidence of long term memory effect for metal futures prices both in SHFE and LME, and this means that metal futures price follows fractional Brownian motion rather than standard Brownian motion.On the assumption that futures prices follow fractional Brownian motion, this paper constructs a fractional pricing model for futures options using quasi-conditional expectation and fractional Girsanov model. Considering the volatility clustering of the metal futures price, it estimates the volatility parameter using GARCH series models based on generalized error distribution. Applying the model to LME copper options, the result shows fractional option pricing model performs more exactly and the volatility based on GARCH model performs better than that based on history volatility. At last this paper analyzes the hedging policy for corporations using commodity options.