FE Problem Set #06
Team Latte Jan 24, 2006
Problem #1
USD/JPY (DollarYen) is supposed to follow the following stochastic differential equation:
Where, is the spot foreign exchange rate and are the volatility and the mean of the spot rate. W is a standard Weiner process.
 Explain the process followed by the foreign exchange rate JPY/USD (YenDollar) such that
 If at time t = 0, the variance of the spot FX rate USD/JPY (DollarYen) is two times the mean (the drift of the spot rate) and its value is 0.1% and if both the USD/JPY and JPY/USD FX rates are at 1.00 then what will be their respective values one year later?
Problem #2
Banco Italiano is offering a 5 year equity linked note that is 100% capital guaranteed at maturity. The note's return is tied to an index and upon maturity the investors will also get 45% of the index growth. If the risk free interest rate is 3%, the annualized volatility of the index is 15% and the dividend yield of the index is 2% what is the price of the structure in percentage terms? What is the price of the embedded derivative (in percentage terms)? Please used closed form BS type model to price the derivative.
Problem #3
Show that the probability density function:
is a solution of the Kolmogorov forward equation:
subject to the boundary condition where is the Dirac delta function.
( Note: This problem is taken from Financial Derivatives ˇV Pricing, Applications and Mathematics by Jamil Baz & George Chacko. This is an excellent book and we recommend it to all .)
Problem #4
(5 year IMCO (a corporate name) trades at 200 bp in the CDS market. Banco Emeraldo is considering issuing a 5 year CLN. The issuing bank's treasury borrows at LIBOR  10 bp for five years' USD or alternatively, suitable collateral can be found paying LIBOR + 15 bp after swap costs. The set up costs for an SPV (special purpose vehicle) is EUR 25,000. The credit structurer is considering the spread that the bank can offer on USD 100 million CLN via (a) limited recourse note programme and (b) an SPV. Discuss.
Problem #5 It is given that the average recovery rate for senior debt is 35% (i.e. on a large portfolio of names with senior debt we would, over time, expect to see that average recovery rate for those that default to be 35%). However, for any particular name the recovery could be anywhere between 0% and 100%. Let's assume that the volatility of the recovery rate is 20%. If we take three recovery rate levels of 0%, 35% and 75%, then what is the probability of a 35% recovery rate?
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