Problem 2: Assume continuous annual risk-free rate is 2% and the current spot price of S&P Index to be $4,289

1. If the continuous dividend yield is 2.5%, what is the prepaid forward price for a contract with 1 years to maturity?
2. What should be the normal forward price on a contract maturing in 3 years?
3. If the observed normal forward price is $5,000, how would you create an arbitrage strategy to take advantage of any mispricing? (buying/selling fractions of a share is ok)

-rxtz orxt: - Dxe -ooix 3 Problem 1 So= $163 ; r = 1 %; D = 10% of So at end of each yo, T= 3 yrs 1. F? So-D xerxt, _ Dr w/ ti=i = $163 - $16.3 x 6 0.01x $16.3xe For too xerxT for is lower than ton (theachical price), then buy for and sell synthetic foward; the wise do the opposite $16 3 1 - 2 2 3 If observed price -0.025%! - Problem 2 S. - $4,289;rl%; S = 2.5%; T=1 1. Fer=Soxe SXT = $4,289 x 2. For = Fo, fx e XT 3 See Problem I point 3 xe Problem 3 C=? for So= $100; K= $100; u = 1.2, d=0.7, 50% 7 2 Can = max( Suu K;o) N-27 -> h=/ Sxu Sun - Suxu= ? T Cu Su Cud - max max (Sud-K;O) 1.+2. S. Sud - Slu= Suxd= ? 4 Sd Sdd = Sdxd = ? dd - max (Suid-K;o) e ? 2 3. Au = ? 4.P -rxtz orxt: - Dxe -ooix 3 Problem 1 So= $163 ; r = 1 %; D = 10% of So at end of each yo, T= 3 yrs 1. F? So-D xerxt, _ Dr w/ ti=i = $163 - $16.3 x 6 0.01x $16.3xe For too xerxT for is lower than ton (theachical price), then buy for and sell synthetic foward; the wise do the opposite $16 3 1 - 2 2 3 If observed price -0.025%! - Problem 2 S. - $4,289;rl%; S = 2.5%; T=1 1. Fer=Soxe SXT = $4,289 x 2. For = Fo, fx e XT 3 See Problem I point 3 xe Problem 3 C=? for So= $100; K= $100; u = 1.2, d=0.7, 50% 7 2 Can = max( Suu K;o) N-27 -> h=/ Sxu Sun - Suxu= ? T Cu Su Cud - max max (Sud-K;O) 1.+2. S. Sud - Slu= Suxd= ? 4 Sd Sdd = Sdxd = ? dd - max (Suid-K;o) e ? 2 3. Au = ? 4.P