Question

What is net dollar gain or cost required to create a short put delta hedge against a 100 short put position? Assume puts are priced at $1.98, the delta is 0.489, the stock price is $34.50, and no cost to short stock.

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Answer 1

Short Put Position means obligation to Buy if Option is exercised. Therefore, we need to Short Stock to Delta Hedge.

Quantity to be sold = Options Sold*Delta = 100*0.489 = 48.9 i.e. 49 shares

As, ther is no cost to short sell, we will receive the proceeds.

Therefore, Net Dollar Gain to Hedge = 49*34.5 = $1690.5

Cross Verification:

Stock Price Declines by $1: In that case, Profit in Short Position = $49 and Loss on Put Position = 100*(1*0.489) = $48.9 i.e. $49

Stock Price Increases by $1: In that case, Loss in Short Position = $49 and Profit on Put Position = 100*(1*0.489) = $48.9 i.e. $49