(Note: Of late, in December 2007, a host of derivatives scandals in India has come to the fore. A lot of small and medium corporations had entered in swap and FX options contracts and have incurred large marked-to-market losses. And they have claimed that the banks there mis-sold the products to them.

*It seems that Indian corporations have, one way or the other, been selling options (or option like products) to banks for quite a few years now (even though the Reserve Bank of India prohibits banks to buy options from corporate customers). In the last couple of years we have seen some really high-risk products that the banks have been selling to the small and medium enterprises. India, it seems, has become the toxic wasteland for financial derivatives.
*

*A recent litigation regarding a USD/CHF product in an Indian court has inspired us to design the following product. The product that we are suggesting below is a high risk product and not suitable for SMEs or risk averse investors and clients. It is suitable for large hedge fund or institutional investors who have the capability and resources to analyze the product and risk manage it.)*

**Realized Volatility linked USD/CHF Options**

The product* is a USD/CHF structure which the client sells to the bank. The clients sells a series of USD puts / CHF calls to the bank all at once with different maturities but in a proportion that is linked to the realized volatility of USD/CHF over the life of the product.

The rationale is that the number of options that the client will sell to the bank is a function of the inverse of the realized volatility. The argument is that if the realized volatility of the FX pair, defined as the standard deviation of the log price relatives (return) for the period preceding the payoff date, falls then the USD/CHF will go up (CHF gets weaker and USD gets stronger) and vice versa. The client is betting on the volatility of USD/CHF dropping and hence profiting from sold USD/CHF option positions. The client is shorting Swiss Franc call options (USD put) and will benefit if the CHF stays at the current level or weakens.

However, the notional of the contracts (the number of the options to be sold) is adjusted by a multiplier which increases as the realized volatility falls and decreases as the realized volatility increases. However, the multiplier is capped on the upside by, say, a cap which is 100% (of the notional).

The product is structured in a way that the contract has a maturity of one year and at time the client sells (shorts) in all twelve USD puts / CHF calls options. The first option has a maturity of one month, the second option has maturity two months and so on; the twelfth option has a maturity of 12 months. These options are not forward start options and all of them start today (at the initiation of the contract), but have different maturities. The only novel feature is that each option will have a different multiplier or the leverage factor (the number of options that the client will sell) which will be multiplied with the notional amount to give the client’s payoff. And this multiplier will be a function of the realized volatility in the period immediately preceding the payoff date.

The payoff of the product, with strike price K and maturity T is given by:

Where, *α* is the multiplier; the number of options that the client will sell and is given by:

In the above *q* is an arbitrary constant. However, we will fix it to the value of the realized volatility (for the past periods) at time *t = 0* , i.e. at the time of the initiation of the contract. If the realized volatitlity of USD/CHF for the past one year has been 9% then we will fix *q=0.09* .

The pricing of the product will be done in a Monte Carlo framework and therefore, starting at time zero, *t = 0 * the FX pair will diffuse with a volatility input that is equal to the realized volatility of the past period (say, the last 252 days). And since *q=0.09* the realized volatility in the coming periods will be benchmarked to 9%, such that if it increases then *q * times the inverse of realized vol go above 100% and if it decreases then *q * times the inverse of vol will be less than 100%. Thus the multiplier will always be capped at 100%.

The choice of is arbitrary and can be adjusted depending on the risk appetite of the client. Also, the strike could be set in such a way that the options are all out of the money and hence could be more speculative in nature. Out of the money options can end up being more expensive owing to volatility skew (it is almost certain that the trader or the client will use vol skew and implied vols to price the options and not past realized volatility).

** This product idea is ours and it is designed by Risk Latte's Analytics team. We believe that no idea, and product ideas are ideas after all, can be patented and copyrighted and therefore should be let out freely in the public domain. And anyway, nine out of ten structurers in large banks and investment banks do nothing but copy each others ideas. The only original ideas that ever came out were the ones from the Bankers Trust guys so many years ago and a handful of French banks of late. But at the same time, due credit should be given to the originator(s) of any idea. If you care to use this idea in any product form, then please do mention our name somewhere. *

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