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.

SHOW ALL WORK

Answer 1

To hedge short put you need to short stocks. When share price goes down, you will lose on short put but will gain on short stock, so your position is hedged.

Number of stocks to be shorted = Number of put * Delta of Put

= 100 * 0.489

= 48.9

So the investor will have to short 48.9 stocks.

Money earned from shorting stocks = Share Price * Number of stocks shorted

= 34.5 * 48.9

= 1,687.05

Premium earned from shorting put = Number of put * premium on each put

= 100 * 1.98

= 198

So total inflow from the strategy = Money earned from shorting stocks + Premium earned from shorting put

= 1,687.05 + 198

= 1,885.05

Net dollar gain is 1,885.05