The price of the European call is c=52×0.7042-50×e-012025×06504=506 b) The initial replicating portfolio consists of N(d,)(long)shares and borrowing of Xe" N(d, ) In this case, the replicating portfolio includes 0.7042 shares and borrowing of $31.56 a) The product provides a Six-month return equal to max(0, 0. 4R), where r is the return on FTSE 100 index. Suppose So is the current value of the index and Sr is the value of the index in six months When an amount a is invested the return received at the end of six months is Amx(0,04*S Sa=044 S maxOS-So) This 0.AA of the European call options on the index with the strike price of So b) with the usual notions, the value of the option offered 0.4A s(Soe - q N(d, )-Soe- N(d2)) 044(eN(d1)-eN(d2) In this case,r=008,q=0.03,=0.25,7=0.50 (008-0.03+0252/2)×0.50 0.2298 025×√0.50 d2=d1-a√T=00530 N(d1)=0.5909 N(d2)=0.5212 The value of the call option is 0.0325A Initial investment: A-0.0325A=0.9675A At six months A Therefore return with continuous compounding Is: 2 In(4 6.6% 0.9675A The return of 6.6% per annum with continuous compound ing is lower than the riskfree rate of interest C Gary Xu AcF2 14 Princip les of finance© Gary Xu AcF214 Principles of Finance 5 The price of the European call is: 52 0.7042 50 0.6504 5.06 0.12 0.25 =  −   = −  c e b) The initial replicating portfolio consists of ( ) N d1 (long) shares and borrowing of ( ). Xe N d2 −r In this case, the replicating portfolio includes 0.7042 shares and borrowing of $31.56. 9. a) The product provides a six-month return equal to max (0, 0.4R), where R is the return on FTSE 100 index. Suppose S0 is the current value of the index and ST is the value of the index in six months. When an amount A is invested, the return received at the end of six months is: max( 0, ) 0.4 max( 0,0.4* ) 0 0 0 0 S S S A S S S A T T = − − This is 0 0.4 S A of the European call options on the index with the strike price of S0. b) With the usual notions, the value of the option offered is: 0.4 ( ( ) ( )) ( ( ) ( )) 0.4 1 2 0 1 0 2 0 A e N d e N d S e N d S e N d S A qT rT qT rT − − − − = − − In this case, r = 0.08,q = 0.03, = 0.25,T = 0.50 0.0530 0.2298 0.25 0.50 (0.08 0.03 0.25 / 2) 0.50 2 1 2 1 = − = =  − +  = d d T d  ( ) 0.5212 ( ) 0.5909 2 1 = = N d N d The value of the call option is 0.0325A Initial investment: A-0.0325A=0.9675A At six months: A Therefore return with continuous compounding is: ) 6.6% 0.9675 2ln( = A A The return of 6.6% per annum with continuous compounding is lower than the riskfree rate of interest