article
October 31, 2014

Equity Linked Instruments (ELI) are becoming very popular investments as they offer investors the potential of earning a high rate of interest while at the same time removing the risk of losing some of their initial investment. This article explains how to value ELI as traded on the Hong Kong stock exchange.

## Three Types of ELI

The payoff of an ELI depends on whether the stock price at maturity is above or below a specified barrier, the strike price. If the barrier is breached, the investor receives an amount of cash based on the interest earned during the life of the ELI; otherwise they instead receive a predetermined amount of cash or quantity of the underlying stock.

There are three types of ELI:

1. The bull ELI offers investors two types of payoffs depending on the value of the underlying price at maturity. If at maturity, the underlying stock price is at or above the strike price, the investor will receive the par value of the instrument, a fixed payment equal to the total investment plus the interest earned during the life of the instrument. On the other hand, if at maturity the underlying stock price is below the strike price, the investor will receive a predetermined quantity of the underlying shares, equal to the par value divided by the strike price.
2. The bear ELI is opposite to the bull ELI. If at maturity, the underlying stock price is below the strike price, the bear ELI pays the par value (again, the total investment plus the earned interest). If at maturity, the underlying stock price is at or above the strike price, the investor receives a cash amount based on a predetermined formula (for example, the par value minus a predetermined number of shares multiplied by difference between the underlying and strike prices, where the number of shares is again equal to the par value divided by the strike price). If, at maturity, the underlying stock price is greater than or equal to twice the strike price, the payoff will be zero.
3. The range ELI is an option for those investors who believe that, at maturity, the stock price will be in a specific range, between lower and upper strike prices. The payoff is equal to the total investment plus the interest earned if, at maturity, the underlying stock price is at or above the lower strike price and below the upper strike price. If the stock price ends up at or above the upper strike price, the payoff will be calculated based on a predetermined formula, as for the bear ELI above. The payoff can be zero if, for example, if the stock price is double or more than the upper strike price. If the closing price does not reach either strike price, the investor will receive a predetermined cash amount or quantity of the underlying stock.

## Valuating ELI with FINCAD software

The following section illustrates ELI pricing examples in FINCAD risk management software by using the aaOption_LV_payoff_eu function. This function allows options with user-defined piecewise linear payoff functions to be valued. Since all the above ELI have such payoffs, it is a simple matter to set the function up to deal with these instruments. Of course, the user has to be careful to specify the payoff table correctly in each case. Different ELI need a different number of points in the payoff table to correctly capture the payoff structure of the instrument. (Note that in all cases, the payoff is extrapolated automatically, in an obvious linear fashion.)

Example - Bull ELI

 Total initial investment $16,965.47 Underlying security Stock A (250 shares) Strike price (underlying security)$70 No. of outstanding days 100 days Potential yield 11.5% Payback if Stock A closes at or above $70 on expiry date$16, 965.47 x (1 + 11.5% x 100/365) Payback if Stock A closes below $70 on expiry date 250 Stock A shares Note that this is the payoff, not the Profit and Loss. Example - Bear ELI  Total initial investment$16,965.47 Underlying security Stock A (250 shares) Strike price (underlying security) $70 No. of outstanding days 100 days Potential yield 11.5% Payback if Stock A closes below$70 on expiry date $16,965.47 x (1 + 11.5% x 100/365) Payback if Stock A closes at or above$70 (ex. at $80) on expiry date$17,500 - 250 x ($80-$70) Payback if Stock A closes at double or more than $70 on expiry date 0 Note that this is the payoff, not the Profit and Loss. Example - Range ELI  Total initial investment$15,608.55 Underlying security Stock A 250 shares Upper strike price (underlying security) $70 Lower strike price (underlying security)$65 No. of outstanding days 100 days Potential yield 15% Payback if Stock A closes below $65 on expiry date 250 Stock A shares Payback if Stock A closes at or above$65 and below $70 on expiry date$15,608.55 x (1 + 15% x 100/365) Payback if Stock A closes at or above $70, e.g.$80 on expiry date $16,250 - 250 x ($80-$70) Payback if Stock A closes at double or more than$70 on expiry date 0

Note that this is the payoff, not the Profit and Loss.

In conclusion, the aaOption_LV_payoff_eu function can be successfully used to price bull, bear and range ELI by setting up the payoff for each specific structure.