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Computer Assignment One

Computer Assignment One - MAFS5250 Computational Methods...

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MAFS5250 – Computational Methods for Pricing Structured Products Computer Assignment One Instructor: Prof Y.K. Kwok * Work as a group of two. _______________________________________________________________________ _ Pricing Behavior of an Equity-Linked Structured Product You are invited to explore the pricing behavior of an equity-linked structured product “24-month callable dual accrual cash or share security on Wal-Mart Stores, Inc and Intel Corp” launched by Merill Lynch in 2008. The product description is outlined below: Issue size: 10,000,000 warrants Minimum subscription: 100,000 warrants Notional Amount: USD 1 per warrant Issue Price: 100% of the Notional Amount Valuation Date: Feb. 11, 2006 Maturity Date: Feb. 19, 2008 The two underlying stocks are Reference price Exercise price Wal-Mart Stores Inc. USD 45.48 USD 39.5676 Intel Corp USD 20.77 USD 18.0699 where Exercise Price = 87% x Reference Price. The Reference Price is taken to be the closing price of the stock on the valuation date. Note that the two stocks have been chosen such that the price processes of them are expected to exhibit minimal correlation. 1. Payoff structure: Full par payment or delivery of the “worst performing” stock on the maturity date. If the settlement prices of BOTH the underlying stocks are higher than or equal to the respective Exercise Price, then each warrant holder receives 100% of the notional amount per warrant held. If either one of the settlement prices is lower than the respective exercise price, then each holder receives per warrant physical delivery of a number of the “Worst performing” stock equal to Notional amount / Exercise Price
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of the worse performing stock. Terminal payoff at time T = min(1, min( S 1 ( T ) / S 1,exer , S 2 ( T ) / S 2,exer )) = 1 - max(1 - min( S 1 ( T ) / S 1,exer , S 2 ( T ) / S 2,exer ), 0), where S 1,exer and S 2,exer are the Exercise Price of Stock 1 and Stock 2, respectively. That is, the investor shorts a put on the minimum of the two stocks. This is a contingent forced conversion which occurs when either one of the two share prices declines. This is just the opposite to that of a convertible bond where the holder of a convertible bond chooses to convert the bond par into shares only when the share price appreciates above certain threshold value. Query: Would the chance of occurrence of contingent forced conversion become higher or otherwise when the correlation between the price processes of the two stocks becomes closer to zero? 2. Additional coupon (accrual feature) The warrant pays out a fixed 4.075% coupon for the first quarter (that is, 16.3% per annum). Afterwards, unless the warrant has been called, over each observation period (3-month period), the holder receives 4.075% x n / N of notional amount where N = number of New York Business Days in the period in the applicable Observation Period; n
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Computer Assignment One - MAFS5250 Computational Methods...

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