Question

Suppose you sell a 45-strike call option at the price of $2.7804, the current stock price is $40 and the call option Δ = 0.5824. The annualized continuously compound interest rate is 8%. If the option is on 100 shares, what investment is required for a delta-hedged portfolio? What is your overnight profit/loss if the stock tomorrow is $40.5 (where call price is $3.0621, and Δ = 0.6142)? On day 2, What is your overnight profit/loss if the stock price is $39.25 (where call price is $2.3282, and Δ = 0.5642)?

Answer 1

For a Delta hedged portfolio we need to buy some amount of share to make Delta=0 ; since we have already sold an option.

Total delta of option= no of shares * delta =100*.5824 =58.24 =58 shares we need to purchase to make a delta hedged portfolio

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Day1:

If stock became 40.5 overnight, our profit /loss = change in stock profit + change in option profit

= 100(2.7804-3.0621) + 58(40.5-40) =.83$ profit

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Day 2

If stock became 39.25 overnight, our profit /loss = change in stock profit + change in option profit

= 100(2.7804-2.3282) + 58(39.25-40) =1.72$ profit