Recently the equity volatilities sky rocketed in Asia. The stock index volatilities across some of the major markets in Asia exploded as a result of market turmoil. Hang Seng Index implied volatility index (as measured by Risk Latte's HiXX^{TM}) crossed 50% in more than a decade.

In such a high volatility regime, investors may find buying options prohibitively expensive. Even the structured products which have stock or stock index options embedded would come with extremely high cost. One particular product, which is essentially a variation of a plain vanilla call option, may be an attractive alternative in such times. It is the amortizing option.

An Amortizing call option has a payoff at maturity like this:

This payoff is attractive during times of high volatility. The payoff is essentially that of a vanilla (European) call option whose notional amount declines as the spot (underlying) goes in the money. The investor gets an exposure to the upside potential of the asset via this option and ends up paying a lot less than he would otherwise do with a vanilla call. Of course, more the option finishes in the money the less is the notional amount of the option. But that may still seem a good trade off in times of high volatility.

As an example we take an ATM vanilla call whose payoff is with strike 100, risk free rate 4.5% and volatility of 50%. We ran it through a Monte Carlo simulator with 1,000 iterations (though in practice one should go up to 30,000 iterations at least) and get a price equal to 21.77%. Next with modify the payoff and take the payoff of the amortizing call option as given above and use the same strike, interest rate and volatility parameters. After a 1,000 iterations, we get a price of 0.11%.

The price of an amortizing call option can be significantly lower than a corresponding plain vanilla option. A replicating portfolio for an amortizing call option is a long vanilla call with a strike of K and short an infinite strip of vanilla call options with strikes from K to infinity.

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