# PnL due to model recalibration and its relationship with hedging error

Consider the case where at t=0, I calibrate my model to the market, but at t=1 my model is no longer able to recover the price in the market, so it needs recalibration. Say I have delta hedged my position. Consider my portfolio PnL in the following 2 situations:

1. I re calibrate my model, and therefore get some PnL due to a change in the portfolio value, which is instantaneous.

2. I choose not to re calibrate it, therefore I get a gamma PnL due to an incorrect delta hedge, which is is not instantaneous but realizes in the next time interval.

Is the PnL in (1) related to the PnL in (2)? How should I choose whether to recalibrate or just accept the gamma PnL?

• If in the second scenario at $t=1$ you mark to market (not model) you also get a PnL right? What I'm getting at, if you mark to market you would also get an instantaneous PnL change. – Bob Jansen Jul 17 '20 at 14:21
• Yes, you would. I think I have gotten something wrong here in situation 2. As far as I thought, the trader can either recalibrate and get a PnL, or he can choose not to recalibrate (and thus not MtM either). Is this incorrect? – Arshdeep Singh Duggal Jul 17 '20 at 14:24
• The trader can choose to not recalibrate and mark to model but this is a bad idea: when the position is eventually closed, market prices have to be paid, not those of the model. It's better to update the parameter and hedge correctly. – Bob Jansen Jul 17 '20 at 14:37
• I suppose then my question is: how is this PnL due to marking to market related to the hedging error, if at all? Obviously one way to quantify it is just the sensitivity*change in parameter value, but is there a relationship with hedging error? – Arshdeep Singh Duggal Jul 17 '20 at 14:41