1.You try to price the call option on XYZ corp. The current stock price of XYZ i
ID: 2790985 • Letter: 1
Question
1.You try to price the call option on XYZ corp. The current stock price of XYZ is $100/share. The risk-free rate is 3%. What is the appropriate price of the 1 year call option of XYZ corp with a strike price of $110 using replicating portfolio approach? You project the stock price of XYZ will either be $100 or $140 in a year. Assume you can borrow or lend money at risk-free rate.
2.You are looking at a call option on IBM with strike price of $155 selling at $3.75 and a put option with strike price of $155 selling at $4.84 (real-time market data on May 7, 2017). Both options will expire on Jul. 21, 2017. What option trading strategy you can employ based on the above two options so you could exploit the possible highly volatile IBM stock price movement in the next three months? Plot the trading strategy profit diagram and point out in what price range your trading strategy will see a profit.
3.
You entered into a long position in 2 corn futures contracts. Each contract size is 5,000 bushels. The initial margin is $4000 in total, and the maintenance margin is $3000 in total. The contract was entered into on June 13, 2012 and closed out on June 17, 2012. Finish the following table:
Date
Future's Price
Daily Gain (Loss)
Cumulative Gain (Loss)
Margin Account Balance
Margin Call ($)
4.00
Jan. 13
3.97
Jan. 14
4.06
Jan. 15
3.92
Jan. 16
3.88
Jan. 17
3.85
Date
Future's Price
Daily Gain (Loss)
Cumulative Gain (Loss)
Margin Account Balance
Margin Call ($)
4.00
Jan. 13
3.97
Jan. 14
4.06
Jan. 15
3.92
Jan. 16
3.88
Jan. 17
3.85
Explanation / Answer
Therefore the Value of Call option (C) can be written as:
C=S+Be-rt….(1)
So Cu=Max(S-X,0)=Max(140-110,0)=$ 30- Value of call in upstate
Cd=Max (S-X,0)=Max(100-110,0)=$ 0- Value of call in downstate
So value of our portfolio in upstate should be 30, while value of our portfolio in down state should be 0.
Therefore, rewriting equation 1 for 2 scenarios (up and down) we get:
×140+Be—0.03×1=30…. (2)
×100+Be—0.03×1=0…. (3)
Now we have 2 equations with 2 unknowns ( and B). Subtraction equation (3) from (2) we get:
×140 =30
-×100=0
40=30
=0.75
Now let’s find the B by plugging in 0.75 in equation 3:
100×0.75+ Be—0.03×1=0
=75+0.970446B=0
B= -75/0.970446
= -77.28409
Therefore current price of the call option using formula 1:
C=S+Be-rt
=0.75×100(current stock price)+ -77.28409e-0.03×1
75-75
=0
2) Closing price of IBM on May 7 is $ 155.
Since we want to benefit from the volatility we have to buy both the call and put option.
Therefore, we would buy 155 strike call for $ 3.75
we would buy 155 strike put for $ 4.84
Net cost for our strategy:
3.75+4.84=$ 8.59
Now this strategy will have 2 breakeven points, one on the upside and one on the downside. So our strategy will give profit once stock price moves beyond these points:
Price of IBM above which strategy will give profit: 155(current stock price) + 8.59=$ 163.59
Price of IBM below which strategy will give profit: 155(current stock price) -8.59=$ 146.41
Stock Price
Profit
110
36.41
120
26.41
130
16.41
140
6.41
150
-3.59
160
-3.59
161
-2.59
162
-1.59
163
-0.59
164
0.41
170
6.41
180
16.41
190
26.41
200
36.41
(The table above range of stock of prices for profit and loss)
3)
Date
Future's Price
Daily Gain (Loss)
Cumulative Gain (Loss)
Margin Account Balance
Margin Call ($)
4
4000
Jan. 13
3.97
-300
-300
3700
Jan. 14
4.06
900
600
4600
Jan. 15
3.92
-1400
-800
3200
Jan. 16
3.88
-400
-1200
2800
1200
Jan. 17
3.85
-300
-1500
3700
Calculations:
Daily Gain (Loss): (Todays Price-Yeserday’s Price)×2×5000
Cumulative Gain (Loss)=Todays Gain Loss+Yesterday’s Gain Loss
Margin Account Balance=Yesterday’s Margin Account Balance+ Daily Gain (Loss)
Note: We will only get a margin call when margin account balance falls below maintenance margin ($3000). In that case we have to refill the margin account till Initial Margin ($ 4000). This happens on Jan 16. So beginning of Jan 17 our margin account balance is $ 4000. We make a loss that day of $ 300. So our ending margin account balance is $ 3700.
Stock Price
Profit
110
36.41
120
26.41
130
16.41
140
6.41
150
-3.59
160
-3.59
161
-2.59
162
-1.59
163
-0.59
164
0.41
170
6.41
180
16.41
190
26.41
200
36.41
Related Questions
Navigate
Integrity-first tutoring: explanations and feedback only — we do not complete graded work. Learn more.