Using Delta to find Option Price Changes
The call option on the $15 strike is currently worth $1.02, and has a delta of 0.43.
How much would the call option be worth if the underlying increases by $0.50?
Hint: Remember that options are long Gamma.
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2 solutions
Why do you think I gave the answer as $1.25 instead of $1.24?
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I hadn't used the hint while solving the problem. Now I understand that long gamma means gamma is positive and not zero, so delta is not linear.
I think that the call option can be worth any price more than $1.235. Is it right? Is there some specific reason for the answer to be $1.25?
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Right, so the delta calculation would give you that the option value is $1.235, and at which point there's the question of "Is the correct answer supposed to be $1.20 or $1.25? Both are close enough, so which one should we go for?"
The reason why $1.25 is a better answer, is because the gamma is positive and so the rate of increase is higher, and those the option value is higher than that obtained just from delta approximation.
The correct formula to use, as stated in gamma is
V s ≈ V S + Δ ( s − S ) + 2 1 γ ( s − S ) 2 .
From this, you can back out what the (approximate) implied gamma is, to obtain a value of $1.25.
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@Calvin Lin – That's an application of the Taylor series expansion right?
Delta-Gamma approximation
Because it's long gamma, meaning the actual price increase will be larger than just 0.5*0.43, so $1.25 is best approximation.
delta increased slightly greater than 0.43
Yes, Aaron's correct. So why the F does the question not provide that as a choice? I rounded it up to the nearest, and it says..."Getting stumped is part of learning." Maybe I'm stumped because the creator of the question wasn't thinking straight.
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The exact number is more than 1.235 because this is a long gamma position, so the delta doesn't stay fixed, it actually increases because the underlying price has risen.
yah yah yah I know. it's 1.99 but there's something wrong. it's actually 5.36. omg it's unbelievable!
dats dumb how day mad 1.25 da answer
😮OMG wy did dey mak 1.25 da answer btw dats dumb😄 just want u tu no dat
wtf wtf wtf wtf wtf dis ding is so hard 😠!
Recall that with respect to call options, delta is defined as the change in price of the call option for $1 increase in the price of the underlying stock.
If the price of the underlying stock had increased by $1.00, the call option price would have increased by delta, i.e. $0.43.
However, since price of underlying stock increases by $0.50, the call option price would increase by 0.50×0.43= $0.22
Hence the call option is now worth $1.02+$0.22 which is approximately $1.25.