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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". $$ (S_T-K_1)\cdot 1_{S_T > K_2} = S_T\cdot 1_{S_T > K_2} -K_1\cdot 1_{S_T > K_2}$$


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 ...


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 ...


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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