PnL due to model recalibration and its relationship with hedging error

Question

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:

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

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?

Bob Jansen · Answer

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, there will be no hedging error even if the market prices are temporarily out of whack.

PnL due to model recalibration and its relationship with hedging error

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