Author_Institution :
Derivatives & Struct. Products, Koch Pet. Group, Wichita, KS, USA
Abstract :
Despite its obvious shortcoming, Black´s formula for futures options is still widely used for pricing energy derivatives. The lognormality assumption that underlies this formula is inconsistent with the market implied distribution for many commodities and as a result, out-of-the-money options are mispriced by Black´s formula. Our objective is to develop a self-consistent term-structure pricing framework based on the general diffusions and derive simple pricing formulas similar to Black´s one with a few additional parameters that can be easily estimated from market prices of liquid options. We assume the following risk neutral dynamics for futures prices: df(t,T)=σ1(f,t,T)dz1+σ2 (f,t,T)dz2, dz1dz2=0. The value of the discounted European call option V(t,f) on T-maturity futures struck at K is determined as the solution to the following diffusion problem ∂V/∂t+½(σ12(f,t,T)+σ 22(f,t,T))∂2V/∂f2, V(T,f)=(f-K)+
Keywords :
costing; diffusion; log normal distribution; modelling; stock markets; T-maturity futures; analytic framework; commodities; diffusion problem; discounted European call option; energy derivative pricing; futures options; liquid options; lognormality assumption; market implied distribution; market prices; out-of-the-money options; pricing formulas; risk neutral dynamics; self-consistent term-structure pricing framework; Arithmetic; Calibration; Closed-form solution; Linearization techniques; Matrix decomposition; Partial differential equations; Petroleum; Pricing; Solid modeling;
