Question

Calculate the elasticity of a call option with a premium of $6.50 and a strike price of $61. The call has a hedge ratio of 0.7, and the underlying stock’s price is currently $47.

Answer 1

The Elasticity of the call option =
`\mathbf{ 5.06 \%}`

Step-by-step explanation:

From the given information:

For $1 change in stock price

the percentage of change in stock price = ΔS/S

ΔS/S = (1× 100)/47 = 2.127659574

ΔC = hedge ratio × ΔS

ΔC = 0.7 × 1

ΔC = 0.7

However , the percentage change in the stock call option price = ΔC/C

= (0.7 × 100) / 6.50

= 70/6.50

= 10.76923077

∴

The Elasticity of the call option =
`\mathbf{(percentage \ change \ in \ the \stock \ call \ option \ price )/(percentage \ change \ in \ the \ stock \ price)}`

The Elasticity of the call option =
`\mathbf{ (10.76923077 )/(2.127659574)}`

The Elasticity of the call option =
`\mathbf{ 5.06 \%}`

OR

The Price Elasticity of the call option can be computed by using EXCEL FUNCTION(=B3*(B4/B1))

The illustration to that can be seen in the diagram attached below.

The Elasticity of the call option
`\simeq` 5.06% by using EXCEL FUNCTION.