We would like to suggest an interesting structure to combine three indices: **Hang Seng Index**, **Nikkei225** and the **DJIA**. The product is a sort of a Mountain Range Note and and contains a Mountain Range option. This kind of a structure is ideally suited for hedge fund managers betting on the short term rise of a basket of assets.

A Mountain Range option, which comes in many flavours, is essentially a variation of a Parisian basket. The option buyer gets a large coupon if no asset in a given asset selection reaches a predetermined limit or barrier during a given time period. Otherwise, the option holder receives the payout of a plain vanilla, or sometimes Asian call on the basket. Sometimes considered as a Parisian basket option due to its barrier and Asian characteristics. The payoff is given as:

Where C is the prescribed payout amount if none of the stocks in the basket hits the barrier during the specified time, X is the strike, i represents the ith stock or asset and *λ* is a binary variable equal to the condition set for the index value as given as:

Where B is the predetermined limit (barrier), t_{1} represents the start of the limit period and t_{2} represents the end of the limiting period.

We can create a principal guaranteed note combining the above three indices which gives a payoff as:

Payoff = N*(1+MR_{call})

Also, we modify the conditions whereby the limiting period is the entire maturity of the note and therefore, t1 and t2 are just t=0 to t=T. The coupon, C, is 5%, the predetermined barrier (limit) is 3.0, the strike rate of the call is 2.85 and the maturity of the note is one year.

**Scenario 1:**

(Mixed Scenario)

As of June 3, 2005 the DJIA is at 10,460, the Hang Seng Index is at 13,818 and the Nikkei225 is at 11,300. The investor buys US$1 million worth of the MR note.

Let us say that after one year DJIA is at 12,000, Hang Seng Index is at 12,896 and the Nikkei225 is at 10,890. This means given a barrier of 3.00 lambda is 1.00 and the payoff of the note is $1,194,220, a return of 19.42%.

**Scenario 2:**

(Very Bullish Scenario)

After one year, say all markets reach short term highs and DJIA is at 12,000, Nikkei225 is at 13,000 and Hang Seng Index is at 15,000. Then the payoff of the MR note will be $1,533,211, a humongous return of 53.32%.

**Scenario 3:**

(Very Bearish Scenario>

After one year, say all three markets crash and DJIA goes to 9,000, Nikkei225 goes to 10,000 and Hang Seng Index goes to 11,000. In this case the payoff of the note is simply the Principal amount as the call option expires worthless.

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