: asset performance at maturity : number of assets

Alternatively,

The payoff looks quite scary at first but let’s visually analyze it for a two asset case where the spot of one of the assets is fixed at the initial spot.

The above figure shows the payoff with spot of asset 2. Observe that the payoff curve has more steepness on the left part (below the fixed spot of asset 1) as compared to the right part (above the fixed spot of asset 1).

Daily Pnl on spot movements will depend on:

- Cash Gamma 1 × ( Realized Variance 1 – Implied Variance 1)
- Cash Gamma 2 × ( Realized Variance 2 – Implied Variance 2)
- Cash Cross-Gamma × ( Realized Covariance 1,2 – Implied Covariance 1,2)

Structure is long gamma, short cross-gamma and both have significant magnitude. When hedging delta, monitor the above three factors along with the amount that you will be losing on theta. In fact one can make money on delta hedging more frequently in case of massive favorable market movements (one of the cases: both the stocks moving by massive amounts in opposite directions and then coming back to their original spot levels)

**Vega**

**Vega of asset 1 v/s spot of asset 1, **clearly structure is short skew.

**Vega of asset 1 v/s volatility of asset 2, both the assets at 100%, **majorly short volatility cross-gamma

**Vega of asset 1 v/s volatility of asset 1, both the assets at 100%, **long

volatility cross-gamma- also intuitive from the payoff

Daily Pnl on vol movements:

- Vol Gamma 1 × ( Realized VolofVol 1 – Implied VolofVol 1)
- Vol Gamma 2 × ( Realized VolofVol 2 – Implied VolofVol 2)
- Vol Cross-Gamma × ( Realized Vol-covariance 1,2 – Implied Vol-covariance 1,2)

Again when hedging Vega, regularly monitor the above three factors and the right time of hedge execution can make all the difference.

Rebalancing vega with spot and vol movements: Basically you find that as long as the vols of different underlying’s move together, variance swaps are a good hedge and you end up making money on rebalancing because there is a bit more convexity on the treasure than on variance swaps. When spots move, it starts to require some rebalancing that generates noise. When vols start to move apart, then it becomes very unstable and you can quickly lose money.

**Correga**

Convexity is just too much at higher correlations. Good luck in hedging this one!

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Great blog and article!

I think you’re missing the payoff graph: “The above figure shows the payoff with spot of asset 2″…but couldn’t see any in the page

looking forward to your next post

Comment by metal_trader — March 1, 2009 @ 12:42 am |