December 29th, 2010, 5:19 pm
For anybody that has read Neuberger's paper, I am slightly confused as to why equation (2) should be satisfied. It seems to indicate that the trader assumes volatility to be a deterministic function of time. Suppose, instead, that the trader believes that volatility is stochastic (e.g. Heston)dS = (Z)^1/2 S dWdZ = k ( m - Z ) dt + a (Z)^1/2 dBdW dB = rho dtThen the price of an option should be a function C(t,S,Z), which satisfiesC_t + (1/2) z^2 s^2 C_ss + k (m-z) C_z + (1/2) a z C_zz + a rho z C_sz = 0C(T,s,z) = F(s)Even if the trader has a view about the current level of volatility (say Zhat), which could be different than the true Z, he can't possibly expect to know Z_t for all t.Any thoughts you have would be helpful.
Last edited by
mattlorig on December 28th, 2010, 11:00 pm, edited 1 time in total.