Frank Inslee, a trader for Seattle Neutral, an option dealer, set up a delta hed
ID: 2806381 • Letter: F
Question
Frank Inslee, a trader for Seattle Neutral, an option dealer, set up a delta hedged portfolio for a written call position one day ago (on day 0). Some details about the delta hedged portfolio are given in the table below. The option is a 90-day European call with a strike price at $110 on AMP, a financial stock, on which Seattle Neutral has written 800 calls when its price was $109/share. The risk-free interest rate is 3%.
Day
Call Premium
Call Delta
AMP Closing Price
Bond Balance
1
3.70
0.47514
108.00
3,240
2
3.44
0.45567
107.50
?
What’s the bond balance on Day 2 after the portfolio has been adjusted according to the needs of dynamic delta hedging?
-4853.
1628.
-1628.
4853.
Day
Call Premium
Call Delta
AMP Closing Price
Bond Balance
1
3.70
0.47514
108.00
3,240
2
3.44
0.45567
107.50
?
Explanation / Answer
Solution:
Option D is correct.
Notice that the stock has fallen from 109, to 108 and then 107.5 per share in three days. So the long position in AMP need to be financed with lower and lower borrowing, i.e. the balance will grow in the positive direction as liability increases.
At the end of day 2 before adjustment:
Long position in AMP stock: 0.47514×800 = 380.112 Shares»381 shares.
New long position in AMP according to the new delta value on day 2:
0.45567×800 = 364.54»365.
Adjustment in AMP shares: 365 - 381 = -16
Cost of purchasing 16 shares more AMP stocks at 44.5/share:-16 ×107.5 = -1,720.
Total bond balance after adjustment = 3,240e^(0.03/365)– (-1,720) =4,853
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