Transcript Exercise - University Carlo Cattaneo
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 15/2/02 22/2/02 15/3/02 15/4/02 15/5/02 15/8/02 15/11/02 3.310
3.310
3.318
3.329
3.349
3.360
3.419
3.499
0.999820
0.999820
0.999170
0.997230
0.994360
0.991580
0.982910
0.973970
02/13/02 02/13/02 02/13/02 02/13/02 02/13/02 02/13/02 02/13/02 02/13/02 11:12:09 11:12:09 11:12:09 11:12:09 11:12:10 11:12:10 11:12:10 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