Q3.
Frank is going to sell his 100,000 Google stock shares in three months. The current price is $5/share. To reduce the risk, he wants to buy a put option. Assume the price of Google share either goes up by 5% or down by 4% each month, though we can’t predict which event will happen exactly. The risk free interest rate is 1% each month. Gina sells Frank a put option. The strike price is 100,000 shares for $500,000.
a) What’s the price of this put option?
b) Describe Gina’s hedging portfolio two months after the option is issued.
Q4.
Carefully state the put-call parity. If put-call parity fails to hold, describe and confirm the arbitrage strategies.
Price 5
3month 1% per month
UP 5%
FSP = Future Spot Price
Down 4%
X or strike price = 5
Upward FSP 5.25
Down FSP 4.8
Situation FSP Vc
I
5.25 -0.25
II 4.8 0
Change 0.45
-0.25
STRATEGY:
WRITE A CALL AND HOLD DELTA SHARES
Calculation of Delta Shares
Delta shares = Change in
VC = 0.555555556
shares
Change in FSP
Future value of portfolio/ maturity value of
Portfolio
Situation FSP Share Value
Vc Portfolio
value
I
5.25 2.916666667
-0.25 2.666666667
II
4.8 2.666666667 0
2.666666667
Now we have created a risk less portfolio as we can see that
the
in both situations the value of portfolio does not change
!
Present value of portfolio
The future value of portfolio is not influenced by FSP and is
certain.
So to calculate Present Value, we can use Riskfree rate (ie
1%)
So value (of portfolio) is discounted using continous
discounting model
2.66666667 / 1.01005 =
2.640133327
Present value of delta shares
Delta shares x Spot price
Delta shares
0.555555556
Spot Price
5
= 2.777777778
Value of call
Value of Portfolio = Value of call + Value of Delta
shares
2.640133 = Vc + 2.777778
Vc 0.137644451
Value of Put
Put Call Parity equation
Vc + PVx = Vp + Vs
Present valueof strike price 5 / 1.01005
4.950249988
So Vp is
0.087894439
PUT CALL PARITY EQUATION
Vp+Vs = Vc+ PVx (where Vp is value of put, Vs is value of shares, Vc is value of call and PVx is Present value of spot price.
NOTE:
If the prices of the put and call options diverge so that this relationship does not hold good, an arbitrage opportunity exists, meaning that sophisticated traders can THEORETICALLY earn a risk-free profit. Such opportunities are uncommon and short-lived in liquid markets.
Q3. Frank is going to sell his 100,000 Google stock shares in three months. The current price is ...
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