18. (6 points) You are a Risk Manager for a US-based trading company with international
operations. The company has the following risk exposures:
•a contract to deliver 1,000 ounces of gold semi-annually for one year at a maximum
price of $400 USD per ounce
•beginning of period 1 year LIBOR (in USD) on a $10,000,000 bank deposit payable
at the end of the year
•7,000,000 Euro receivable from financing a customer purchase due in 1 year
You are given the following information:
•Available hedging instruments include currency forwards, USD swaps, and gold
options.
•Current exchange rate = .75 Euro / $1 USD
•Risk free rates USD Euro
6 month 2.5% 4.0%
1 year 3.0% 5.0%
Swap rates (USD) Floating rate Fixed Rate
6 month LIBOR 2.75%
1 year LIBOR 3.25%
•Option price per 1 ounce go ld contract with strike of USD 400:
Buy
Call
Sell
Call
Buy
Put
Sell
Put
6 month 4.0 3.6 6.0 5.2
1 year 6.0 5.6 8.0 7.2
(a) Describe the advantages of managing risk of strategic exposures in general as
defined in Chew.
(b) Propose a methodology to completely hedge the company against its strategic
risks.
(c) Calculate the market value of the risks in USD.
COURSE 8: Fall 2004 -19- GO ON TO NEXT PAGE
Investment
Afternoon Session
19. (6 points) BB No-Show Inc, a US company, is negotiating to buy a Japanese company.
The deal is expected to be closed in 3 months, with cash payment in Japanese Yen.
The chief financial officer of BB No-Show Inc has decided to buy an at-the- money call
option on Japanese Yen to hedge against a sudden increase in Yen relative to the US
dollar.
You are given the following information:
•Option type: at-the-money European call option.
•Maturity date of the option: 3 months (65 trading days)
•The option-holder has the right to buy 220 billion of Japanese Yen.
•US Treasury bond rates are 1% compounded continuously
•Japanese government bond rates are 0.05% compounded continuously
•Current exchange rate: 1 USD = 110 Japanese Yen
•Japanese Yen / USD exchange rate has daily volatility of 0.62%
An asset price S follows the stochastic process dS mSdtsSdz
(a) Apply Ito’s lemma to derive the process followed by G = S exp rTt
where r is the risk- free rate and Ttis the time to maturity.
(b) Interpret the derived stochastic process if G is a stock paying dividends at a
continuous rate.
(c) Define the stochastic process of G in the risk neutral world, assuming G is the
spot foreign exchange rate.
(d) Calculate the value of the call option using the applicable Black-Scholes formula
for this call option on Japanese Yen.
COURSE 8: Fall 2004 -20- GO ON TO NEXT PAGE
Investment
Afternoon Session
20. (3 points) You are given the following information at time t = 0:
•Total assets supporting participating life = $74,081,822
•Total participating life liabilities = $66,673,640
•Maturity of policy = 10 years
•Guaranteed interest rate of the policy = 3% continuously compounded
•10-year European call option values for an asset with current price
$74,081,822:
Strike price Call Value
$85,000,000 $8,520,220
$90,000,000 $7,625,000
$95,000,000 $4,502,535
$100,000,000 $1,204,330
$105,000,000 $820,300
Calculate the equilibrium participation level for policyholders.
**END OF EXAMINATION**
AFTERNOON SESSION

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