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If you consider delta, gamma and vega as three variables, and you are able to construct a portfolio with any values, i.e. with three degrees of freedom: $$ [\delta, \gamma, \theta]$$ And you have a space of products which allow you to construct a hedge for any such delta and vega then you must have at least these two degrees of freedom (in some basis): $$ ...


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This is one of those situations that is not practically possible but is possible in theory. For example , the contingent payoff at $T=20$ is just $S_(20)$. But the world is such that at t=11, the stock is negatively correlated with interest rates to such an extent that the forward price $S(11,20)$ observed at t=11 for the stock at T=20 actually moves in ...


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In Black-Scholes world, we have: $$V_y= \sigma_y \tau_y S^2 \Gamma_y $$ and similarly for $z$.


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What you are probably looking for is DV01 based hedging. Let's suppose your delta risk strip is defined as the market value impact of +1bp shift in the par instruments. As an example, suppose you have a risk of -5k DV01 in the 5Y bucket. In order to completely hedge this -5k DV01 risk, your hedge needs to have +5k DV01 risk. Assuming zero interest rates, ...


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Yes, there are new ways to mitigate this since the CHF blowout a few years ago. Some people realized back then that there was a way to game retail FX brokers by having opposite leveraged positions and not paying negative balance. For instance, some brokers set up a fixed liquidation execution price that is less favorable than the liquidation trigger price. ...


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I'll start by saying that if you found a cheaper way to hedge exactly the same risk, that would be arbitrage (assuming transaction costs don't invalidade the opposite position) Without going into the numbers, although the pull to par effect is not very relevant here, you will always have basis risk so you can't really tell beforehand which is the best ...


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