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Foundations of Financial Markets

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1. Duration for the coupon bond:
D= 2501.2510001+2501.25210002+12501.25310003=2.44

The percentage change from 25% to 26% for the zero-coupon bond is shown as
ΔPP=-2.51.250.01=-2%

The percentage change from 25% to 26% for the coupon bond is shown as
ΔPP=-2.441.250.01=-1.95%

The zero-coupon bond is more sensitive to interest-rate change due to its longer duration.

2. (a) An investor wants upside potential if IBM increases but wants (net) losses no greater than $15 if prices decline. ST | 100 | 110 | 120 | 130 | 140 | 150 | 160 | 170 | 180 | 190 | 200 | Payoff | 0 | 0 | 0 | 0 | 0 | 0 | 10 | 20 | 30 | 40 | 50 | Profit | -15 | -15 | -15 | -15 | -15 | -15 | -5 | 5 | 15 | 25 | 35 |

(b) An investor wants to capture profits if IBM declines in price but wants a guaranteed limited loss if prices increase. ST | 100 | 110 | 120 | 130 | 140 | 150 | 160 | 170 | 180 | 190 | 200 | Payoff | 50 | 40 | 30 | 20 | 10 | 0 | 0 | 0 | 0 | 0 | 0 | Profit | 35 | 25 | 15 | 5 | -5 | -15 | -15 | -15 | -15 | -15 | -15 |

(c) An investor wants to capture profits if IBM declines in price and is ready to accept unlimited losses if prices increase. Further, the investor wants to break even if the stock price does not change between now and the maturity of the options. ST | 100 | 110 | 120 | 130 | 140 | 150 | 160 | 170 | 180 | 190 | 200 | Payoff | -100 | -110 | -120 | -130 | -140 | -150 | -160 | -170 | -180 | -190 | -200 | Payoff | 50 | 40 | 30 | 20 | 10 | 0 | -10 | -20 | -30 | -40 | -50 |

(d) An investor wants to profit if IBM's upcoming earnings announcement is either unexpectedly good or disappointingly bad. ST | 100 | 110 | 120 | 130 | 140 | 150 | 160 | 170 | 180 | 190 | 200 | PayoffC | 0 | 0 | 0 | 0 | 0 | 0 | 10 | 20 | 30 | 40 | 50 | PayoffP | 50 | 40 | 30 | 20 | 10 | 0 | 0 | 0 | 0 | 0 | 0 | PayoffT | 50 | 40 | 30 | 20 | 10 | 0 | 10 | 20 | 30 | 40 | 50 | Profit | 20 | 10 | 0 | -10 | -20 | -30 | -20 | -10 | 0 | 10 | 20 |

3. (a) .6 S1 = $130 .6 P1 = max{S1-X,0} = $0 S0 = 100 P0 = $4 X = $90 .4 S1 = $80 .4 P1 = max{S1-X,0} = -$10 Trade | T=0 | T=1; ST = 80 | T=1; ST = 130 | Stock | -100 | +80 | +130 | Buy 5 Puts Buy Bond F=130 | 5C0 = 20 -130e-r | -50 +130 | 0 +130 | Total Payoff | -100 | +80 | +130 | -130e-r + 20 = -100 r = 8% (b) The risk free rate would still be 8% because the probabilities do not influence the risk free rate. The condition of no-arbitrage is still the same.

4. (a) With a high interest rate, as T increases from 1 to 2, the price of the put lowers. On the other hand, when the interest rate decreases, the put price increases. The higher the interest rate, the more investors would want to hold onto their risk-free assets. Therefore, the greater the time is to expiration, the greater the opportunity cost there is for investors to hold onto their options.

(b) The call price is always increasing when the time to expiration increases because buying call options delays investing in the underlying asset until expiration date. This gives the investor more time to invest in other risk-free assets.…...

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