### 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

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