Kindly explain what is meant by delta-normal model understates the probability of high option values and understates the probability of low option values. Thank you.
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,
Kindly explain what is meant by delta-normal model understates the probability of high option values and understates the probability of low option values. Thank you.
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