Delta Hedging

Incorrect. This is 525 multiplied by 35, but this does not represent the relationship of a delta hedge. Consider the relationship of the number of shares needed for a delta hedge as a function of the number of shares represented by the call option contracts and the estimated delta of the call options: $$\displaystyle N_S = -N_C \frac{\Delta C}{\Delta S} = N_C (Delta) $$

A delta hedge is constructed on a short call position by purchasing 525 shares of stock, due to the option's delta being approximated as 0.35. The short call position represents approximately how many shares?

Incorrect. If the calls represented 525 shares of stock, then the delta hedge would involve the purchase of 184 shares. But this is in reverse: the 525 shares have been purchased _as_ the delta hedge to cover a larger number of shares represented by the short call option position.

Correct! The number of shares needed for a delta hedge is based on the number of shares represented by the call option contracts and the estimated delta of the call options: $$\displaystyle N_S = -N_C \frac{\Delta C}{\Delta S} = N_C (Delta) $$ Given that 525 shares were purchased as a delta hedge for option contracts with a delta of 0.35, the number of shares represented by the call options can be solved for as: $$\displaystyle 525 = -(-N_C)(0.35) $$ $$ N_C = \frac{525}{0.35} = 1,500 $$

184

1,500

18,375