1. You intend to value a European call option: Given the following data: Exercise
price E = 100 RMB, price of the underlying at t = 0 100 0
S = RMB, u = 1.1, d = 0.8,
i = 0.05. u and d are assumed to be constant over time.
a) Compute the value of a European Call Option after one, two and three
periods!
b) Compute the value of the corresponding European put options!
c) What would be the result of your computation if the interest rate i would be
11 % (instead of 5 %)?
2. Given Black-Scholes formulae for a European call option with the notations from
the lecture:
a) Derive the formulae for a European put option (using put-call-parity)
b) What is the delta-factor?
c) Explain briefly how Garman-Kohlhagen formulae is derived from Black-
Scholes formulae!
3. Suppose your bank sells 1,000 call options and 1,000 put options to a client. You
want to hedge your net position by delta-hedging. You value your call and put options
by Black-Scholes formulae.
The initial data is:
S0 =100 ; E = 100; s =0.1;  i =0.05.
The following prices of the underlying were recorded (additionally, you find the values
of the standard normal distribution):
Time in days 90          70           50            10              5
          S         100        95          105           96            106
         d1        0.273   -0.930     1.522       -2.375        5.043
         d2        0.223   -0.974     1.485       -2.392        5.031
       Phi(d1)   0.608   0.176      0.936        0.009       1.000
       Phi(d2)   0.588   0.165      0.931        0.008       1.000
Explain at each time step what you are doing to create a risk neutral portfolio!
4. Suppose the exchange rate in t = 0 is 1 Euro = 1.18 Euro. The annual interest rate
in the U.S.A. is assumed to be 3.75 % in year one and 4 % in year two while
European interest rate is 2.00% and 2.25 % in year one and two, respectively.
a) Derive the futures price of USD in Euro in 2 years!
b) Suppose the Euro is forward, i.e. in two years, overvalued. Show at a self-chosen
example the arbitrage process!