Optimizing Vertical and Calendar Spreads

Hi,

Verticals – Manage Delta
Horizontal – Manage Theta
Diagonals – Manage Vega

Vij = option at month i and strike j
Wij = weight of option at month i and strike j

V(S, τ, r, σ) = ∑ ∑ Wij * Vij(Kj, S, τ, r, σ)

Maximize the expected value of the portfolio under lognormal return expectation (If the maximum loss is bounded, lognormal assumption is conservative; if not disastrous)
Minimize the bound of the maximum loss
Maximize Speed

S.t.
Maximum loss is bounded at L
L < maximum loss entertained
V < 0 (cash out flow –ve i.e. there is an initial cash inflow)
Delta = 0
Vega = 0
Gemma > 0
Volga > 0
Gamma Gamma > 0

Any comments

Best Regards, Suminda