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To do this, you need to find some securities that depend only on the risk-free rate, and calibrate your risk-free rate curve to them, and then use that rate to price your options. In this way, your model will exactly reprice at lease two types of security. There are many choices, but the easiest is government bonds in the currency of interest to you. You ...


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To continue the discussion in the comments but in order to not put answer there: Section 2.6 from these notes by Mark Davis mentioned in this question describes hedging error in the Black-Scholes world. There is no direct relation between marking to market and hedging error. If you continuously hedge and have a perfect model which is correctly calibrated, ...


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Usually multidimensional objective function of calibration error of stochastic volatility models (Heston , bergomi etc) have many local minima, thus you would get similar calibration error for very different set of parameters. Some ways to deal with it: specify paramter range your are comfortable with. let's say you want your vol of vol to be in the region ...


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