Exam questions 13 Jan 2011

1)
a) (1 point) Suppose an investor has a forward currency exchange contract, which states that he shall sell 100 000 GBP in exchange for dollars at a rate of 1.9$/GBP. At maturity, the exchange rate is at 1.89. What is the gani/loss for the investor (answer: 1000 gain)
b) (1 point) What is the current level of the BEL 20, and how has it performed over 2011 (answer: about 2000 now, has been at 2700 beginning of 2011, dropped mostly in summer)
c) (1 point) What is the rate on 10year bunds, and what is the rate on belgian 10y bonds (answer: I think it was about 1.5% vs. 4% at first Jan 2012, but I think spread has widened again since then)
d) (1 point) Bank quotes a 10% rate on a product, paid quarterly, what is the continuously compounded r which corresponds to it? (answer = (ln(1+2.5%))^4)
2)
a) (2 points) Give pay off of long one call option at K=100K and short one call option at K=110 (answer: 0 for S<100, 10 for S>110, linear between)
b) (2 points) Give 6 factors that determine price of american put on dividend paying stock and if the parameter goes up, what does price of AP do (vol +, T +, K +, S -, r -, q +; I'm not sure about +/- everywhere, but think most of them are correct)
3) (4 points)
Prove that exercising an American Call is never optimal, using non arbitrage argument
4)
a) (2 points) calculate value of given down and out call option (sigma given, r given) using 2 period tree
b) (1 point) give BS formula for European Call
c) (2 points) if vol per annum is 30%, what is vol at one trading day (answer = 30%/sqrt(260), assuming 260 trading days) and what is daily variance of percentage return on stock (answer: this is exactly the same thing)
d) (3 points) given the BS SDE dX = mu dt + sigma dW, derive the BS PDE, using a portfolio hedging argument (no idea how to do this :-))