Limitations of the Delta- Normal approach
- Thread starter PMuir6307
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@PMuir6307 We have many discussions about this under the "delta-normal" tag https://forum.bionicturtle.com/tags/delta-normal/ ; e.g., in particular good is this discussion https://forum.bionicturtle.com/threads/p1-t4-328-delta-gamma-value-at-risk-var-allen.7203/
And I have a video on delta-normal VaR at https://forum.bionicturtle.com/threads/t4-03-delta-normal-value-at-risk.22462/
Below is Hull's Fig 19.2. For example, if you have a call option on a stock at S(0) = $100 while the Δ = N(d1) = 0.60, then a "delta-normal" approach says: if Stock increases to $110.00, then the option price increases by $10*0.60 = +$6.00, but the actual price will higher due to the curvature (gamma). That is the gist ....
However, when saying "understate/overstate" in context of value/VaR, you have to be very careful about interpretations. For example, the meaning of "understates the probability of low option values", to me, is slightly ambiguous (even if I wrote it somewhere!). Setting aside the exact meaning of "probability" in this sentence, you can see how what's true is "the delta-normal approach will overstate the loss in value of a call option" which could be said to mean "the delta-normal approach will under-price a call option when the stock price drops." Thanks,
And I have a video on delta-normal VaR at https://forum.bionicturtle.com/threads/t4-03-delta-normal-value-at-risk.22462/
Below is Hull's Fig 19.2. For example, if you have a call option on a stock at S(0) = $100 while the Δ = N(d1) = 0.60, then a "delta-normal" approach says: if Stock increases to $110.00, then the option price increases by $10*0.60 = +$6.00, but the actual price will higher due to the curvature (gamma). That is the gist ....
However, when saying "understate/overstate" in context of value/VaR, you have to be very careful about interpretations. For example, the meaning of "understates the probability of low option values", to me, is slightly ambiguous (even if I wrote it somewhere!). Setting aside the exact meaning of "probability" in this sentence, you can see how what's true is "the delta-normal approach will overstate the loss in value of a call option" which could be said to mean "the delta-normal approach will under-price a call option when the stock price drops." Thanks,
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Sixcarbs
Active Member
Do you have a source for this statemen?
Are high option values anything deep in the money?
Are low option values anything out of the money?
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