Demonstrate, that for a volatility surface b(K, T ) which is nonarbitrageable everywhere according to a proportional dividend model, that the sticky delta transformation under spot shock S SS will preserve the no arbitrage conditions for arbitrary spot shock (Hint consider the Dupire local vol formula ) '(K,T) (KS S',T)

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Question: Demonstrate, that for a volatility surface b(K, T ) which is nonarbitrageable everywhere according to a proportional dividend model, that the sticky delta transformation: under

Demonstrate, that for a volatility surface bσ(K, T ) which is nonarbitrageable everywhere according to a proportional dividend model, that the ‘sticky delta’ transformation:

'(K,T)=(KS/S',T)

under spot shock S = S′−S will preserve the no arbitrage conditions for arbitrary spot shock. (Hint: consider the Dupire local vol formula.)

'(K,T)=(KS/S',T)

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