Using Gamma to find Option Price Changes
Quantitative Finance
Level
2
When the stock is trading at $115, the put option on the $113 strike with 30 days to expiry is worth $1.34. It has a delta of -0.3357 and a gamma of 0.062.
How much would the put option be worth if the underlying increases to $117?
$0.793
$0.669
$0.917
$0.545
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1 solution
Δ ( S ) = ∫ Γ ∂ S = 0 . 0 6 2 S + C Substitute S = 1 1 5 and Δ ( 1 1 5 ) = − . 3 3 5 7 to get Δ ( S ) = 0 . 0 6 2 S − 7 . 4 6 5 7 Next, since V ( S ) = ∫ Δ ( S ) ∂ S , V ( S ) = 0 . 0 3 1 S 2 − 7 . 4 6 5 7 S + C Substitute S = 1 1 5 and V ( 1 1 5 ) = $ 1 . 3 4 to get V ( S ) = 0 . 0 3 1 S 2 − 7 . 4 6 5 7 S + 4 4 9 . 9 2 1 Finally, to find V when the underlying is $ 1 1 7 , substitute S = 1 1 7 to get V ( 1 1 7 ) = $ 0 . 7 9 3