Generally accepted theoretical consensus is that asset pricing is a random walk.

But for all practical purposes this might not be true. A practical scheme must capture:

• Mean reversion trends

• Serial correlation

• Price elasticity of variance

• Stochastic volatility

• Return correction component

• Jumps

And the effects of the above change with continuously. Therefore, the calibration will also need to be dynamic.

Modeling all this in a mathematically proven model is difficult, but still computer simulations can be done using soft techniques which profile the needed parameters given the situation. The parameters estimation can be done based on situational set for each parameter. The ideal method to do this is subjected to further investigation.

The type of process which needs representing in discretized for is:

(S(t) – S(t – 1) / S(t)) (1 – ξ Δt) = ά (μ* – μ) [S(t) ^ (Θ1 / 2 – 1)]Δt + (ρ – 1) S(t – 1) / S(t) + [S(t) ^ (Θ2 / 2 – 1)] σ1 Δ W + ή (κ + σ2 ΔB) / S(t)

0 <= ρ <= 1 (ρ = 1 and ξ = 0 and Θ1 = 2 then diffusion process)

Best regards, Suminda Sirinath Salpitikorala Dharmasena

Labels: Asset Pricing, Derivatives