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3

Long gap call option position is the same as long an asset-or-nothing digital option and short a cash-or-nothing digital option, both "classical". $$(S_T-K_1)\cdot 1_{S_T > K_2} = S_T\cdot 1_{S_T > K_2} -K_1\cdot 1_{S_T > K_2}$$

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I'm not sure I understand the question, but I'll give it a try anyway. The mean and variance specified for the terminal distribution $S_T$ are dependent on current asset price, $S_0$, and implied volatility, $\sigma_i$ (which needs to come from the market via hopefully same pricer that one uses). The expectation of a payoff, function $f(S_T)$, is hence a ...

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A model 'understands' the price of risks that are assumed to exist. For example, the Black-Scholes model undertands the cost of delta-hedging, but not of vega-hedging. Hence we have stochastic volatility models: these understand the cost of delta-hedging and volatility hedging. However, none of these models take into account transaction costs. Hence you ...

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Since the correlation matrix is symetric, if you move the term (i,j), you have to do it for the term (j,i) as well Of course -> the correlation of an asset with itself is equal to 1... so it should not change You apply a downward shock (1 to 0.99) and you use the formula of finite differences

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