Suppose S=25, sigma=32%,r=4%,delta=0%, and T=182 days. Suppose you buy a 23-strike put.
In the Black Scholes world, the delta of a call option is given by N(d1)
and the price of the call option is given by:
Please look at the snapshot from my model below:
Hence, delta of the call option = N(d1) = 0.715747
The option is on 100 shares. Let's say we need to short = Number of shares under call option x Delta of the call option / Delta of the stock = 100 x 0.715747 / 1 = 71.57 number of shares.
Hence, we need to short (sell) 71.57 number of shares to create a delta hedged portfolio.
Hence, investment required for a delta-hedged portfolio = Cost to buy option on 100 shares - proceed from short sell of 71.57 shares = 100 x C - 71.57 x S = 100 x 3.58 - 71.57 x 25 = - 1,430.95
The negative sign signifies that there will be an inflow of 1,430.95 on creating a delta hedge portfolio.
When S = 24.552:
Your overnight profit = 100 x Vcall - 71.57 x S - initial investment = 100 x max (S - K, 0) - 71.57 x 24.55 - (-1,430.95) = 100 x max (24.55 - 23, 0) - 326.35 = 100 x 1.55 - 326.35 = - 171.35 (i.e there is a loss of 171.35)
When S = 26.25:
Your overnight profit = 100 x Vcall - 71.57 x S - initial investment = 100 x max (S - K, 0) - 71.57 x 26.25 - (-1,430.95) = 100 x max (26.25 - 23, 0) - 447.89 = 100 x 3.25 - 447.89 = - 122.89 (i.e there is a loss of 122.89)
Suppose S=25, sigma=32%,r=4%,delta=0%, and T=182 days. Suppose you buy a 23-strike put. Suppose S=25, sigma =...
Suppose S = 25, sigma = 32%, r = 4%, o = 0%, and T = 182 days. Suppose you buy a 23-strike call. What is delta? If the option is on 100 shares, what investment is required for a delta-hedged portfolio? What is your overnight profit if the stock price tomorrow is S = 24.552 What if the stock price is $26.25?
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