108156.pdf

210 Mathematics for Finance

Figure 9.5 Decomposition of a target payoff into options

and down price jumps. We also assume for simplicity that there are 360 days in
a year. The risk-free return over 20 days isrF∼= 0 .6316%. (Implied by the effec-
tive rate of 12%.) The $15,000 invested without risk would become $15, 094. 74
at the end of the 20-day period. Consider the following risky investments:

1.Stock.An investment in stock should bring an expected return ofμS∼=

1 .5115%. (Equivalent to 31% annually.) Buying 250 shares, the investor

wouldexpecttoendupwith$15, 226 .72 after 20 days. The risk can be

estimated from the option price, see below.

2.Call Options.A more risky alternative is to buy call options. The return