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