Exercise
Lecture 1
fwd/futures price
Cash and futures market (mib30; h 11:57 13 feb?)
Can I answer to the question: is there an arbitrage
opportunity?
answer
• no! I need: contract expiry date; interest rate
level and dividend yield
first data ...
• expiry date: 15 mar 02 and 21 jun 02
• interest rates:
EURZ=R
EURTNZ=R
EURTNZ=R
EUR1WZ=R
EUR1MZ=R
EUR2MZ=R
EUR3MZ=R
EUR6MZ=R
EUR9MZ=R
MATURITY DATE PRIM ACT 1 SECOND ACTIVY 1 VALUE DATE 1 VALUE TS1
15/2/02
3.310
0.999820
02/13/02
11:12:09
15/2/02
3.310
0.999820
02/13/02
11:12:09
22/2/02
3.318
0.999170
02/13/02
11:12:09
15/3/02
3.329
0.997230
02/13/02
11:12:09
15/4/02
3.349
0.994360
02/13/02
11:12:10
15/5/02
3.360
0.991580
02/13/02
11:12:10
15/8/02
3.419
0.982910
02/13/02
11:12:10
15/11/02
3.499
0.973970
02/13/02
11:12:10
some necessary math
• I have to calculate:
• exp[(r-q)*T]= exp[r*T]*exp[-q*T]
• Now, exp[r*T]=inverse of the discount
factor=1/0.99723=1.002778
• F=30481*1.002778*exp[-q*T]
• F=30565.67 *exp[-q*T]
• in our case: F is quoted and it is equal to
30500
... a complicated world
• then we need to know q. But q is not a
tradable good, so we need to find its implied
value and think if it makes sense or not
• implied q: exp[-q*T] =30500/30565.67
• -q*T=log(0.997852)=-0.002151
• q=0.002151 / T=0.002151 / (1/12)
• implied q= 2.58%
arbitrage decision
• if we think that q will be 1% (< implied q), I
should buy the futures (& sell the stocks). In
fact, for me the real value of the futures
should be:
• 30481*1.002778*0.999167= 30540>F
• With my strategy, I will pay 30500 on
March 15, so that if my estimate of q is
correct, I will have a net profit of 40