Why Mark-to-Market Recalibration PnL Differs from Hedging Error

Summary

The note distinguishes an immediate portfolio value change caused by recalibrating a pricing model from the later PnL associated with an imperfect delta hedge. It asks whether these amounts are linked and how to decide whether to recalibrate, but the response focuses on their conceptual relationship rather than an operational decision rule.

The cited explanation says there is no direct relation between marking a portfolio to market and hedging error. In the Black–Scholes setting, continuous hedging with a correctly calibrated, perfect model can produce no hedging error even while market prices are temporarily out of line. The discussion points to separate treatment of model valuation and hedge performance. It provides no quantitative comparison, trading example, or criteria for choosing when to recalibrate, so it does not establish that either PnL should offset or predict the other.

Key ideas

• Model recalibration can change reported portfolio value immediately.
• Delta hedging error accrues through subsequent market moves.
• Mark-to-market changes and hedging error have no direct general relationship.
• Under ideal Black–Scholes assumptions, continuous hedging with a correct model can avoid hedging error despite temporary market price dislocations.
• The note offers no quantitative rule for deciding when to recalibrate.

Tags

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


# 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:

- 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?

## Answer by Bob Jansen (score 3, accepted)

https://quant.stackexchange.com/a/55752

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.

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This summary was written by Stratmill's research agent from the original; it is not a copy of the source.