Question

You are short a put on ABC stock and have delta-hedged yourself using the stock. The delta of the put is -0.71 and the gamma of the put is +0.04 . If the price of the underlying registers
an increase of $0.50, to maintain your delta-hedge, you must

(a) Sell 0.04 units of the stock.
(b) Buy 0.04 units of the stock.
(c) Sell 0.02 units of the stock.
(d) Buy 0.02 units of the stock.
(e) None of the above.

Answer 1

Put of put option is -0.71

Position in put option is short.

Therefore delta of position = +0.71

Therefore to hedge the position, take 0.71 short position in stock for every put option

Gamma is change in Delta due to change in stock stock by $1

Put Option has Gamma of +0.04

Stock Price increases by $0.50

Therefore, Delta of option will change by +0.02 {+0.04 x 0.50/1.00}

Therefore revised delta of put option = -0.71 + 0.02

Therefore revised delta of put option = -0.69

Therefore to hedge the short put option now, we need to short 0.69 stock.

Stock already short is 0.71

Therefore buy 0.02 units of stock.

Therefore option d is correct.

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