You work in a quantitative group of a small European bank. Your section head has asked you to come up with a pricing and hedging method for a certain OTC derivative product. She has asked you to prepare a report for her describing (i) the pricing method, (ii) the hedging strategy, and giving (iii) some numerical examples, both of the hedging strategy and of benchmarking results. She has made it clear that your performance will be reflected both in your bonus and in her view of your suitability for the job.
The option is an exotic partial barrier option written on an FX rate. The current value of the underlying FX rate is 1.45 (that is, 1.5 units of domestic buys one unit of foreign). The option matures in one year. The option:
i) knocks out if the FX rate is less than a lower barrier level L < 1.45 at any time in the period between four months time and eight months time;
ii) converts into a put with strike XP = 1.55 if the FX rate exceeds an upper barrier level U > 1.45 at any time in the period between four months time and eight months time. It cannot then be knocked out even if the lower barrier is subsequently hit;
iii) has a call option payoff with strike XC = 1.5 if it hits neither barrier.
The values of U and L and determined from your ID number. If n is the final digit of your ID number and m is the penultimate number, set
U = 1.55 + n/100
L = 1.25 + m/100
For concreteness assume the drift of the FX rate (under risk neutrality the difference between the domestic and foreign riskless rates) is constant with value = 0.02. Assume its volatility is = 0.15.
Your section head puts up with little nonsense. The report should be focused and tight; your section head detects the slightest hint of waffle and shouts very loudly at the perpetrator. You should clearly describe the pricing method, giving well chosen numerical examples of it at work, convincing the reader that the prices are accurate. The hedging method may involve spot or other options but (i) should be clearly defined and (ii) work, within reason (the hedge is not expected to be perfect). You should discuss the efficiency and robustness of the hedging strategy, for instance, when it would fail to work, how costly it could be (eg, how much trading it entails), how difficult it would be to follow.
You are free to devise whatever pricing method and hedge you like. An acceptable approach is to adapt Monte Carlo spreadsheets supplied in the module to supply illustrative, tentative prices. In this case a standard error should be reported but no attempt is required to reduce the standard error to levels acceptable in industry. You should however comment on the effect on the price of the number of time steps and sample paths used in the illustrative valuation.
The criteria is (i) does the method work and (ii) can you explain it clearly and convincingly. You should undertake research to provide guidance on possible hedging and pricing strategies.
You should display (i) a knowledge of the relevant theory, derived from both textbooks and articles published in academic journals, and (ii) an adequate set of IT skills (eg at spreadsheet level).
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