For business school students taking the treasury product exam or preparing for a trading desk interview, the USD JPY pair is particularly troublesome. Here is a list of common errors and challenges side by side with four simple examples for options on the USD JPY pair that we hope would clear the frustration around this pair.

For example when the call option is on USD see example 1 , i. But what is the appropriate convention for Spot and Strike exchange rates? In like manner for the equivalent put option on JPY see example 2 , i. Again what is the appropriate Spot and Strike rate conventions? After determining the appropriate currency convention to use in the option pricing formula, another point of confusion is with regard to the risk free rates. After calculating the premium a common confusion is wrt the currency in which the premium is expressed.

Again we look at the currency convention used in the call and put formulae. Total option contract value. Following on point 3 above, another error lies in calculating the total contract value of the option.

Will USD notional be converted using the initial spot rate or the strike rate? One way to decipher this is to think of how you would have to rewrite the product term sheet for the inverted currency convention with notional expressed in JPY terms at the same time maintaining equivalency between the two term sheets?

What JPY notional will make the two product term sheets the opposite sides of the same coin? The original term sheet speaks of an exchange of currency at a pre-defined strike exchange rate.

In particular, for a call option on USD that is exercised, the customer will buy USD at the exchange rate of This means he will sell JPY , The notional amount is USD Currency convention and intrinsic value In general, the intrinsic value of a call option is max S T -K, 0 while that of a put option is max K- S T , 0 For example when the call option is on USD see example 1 , i.

If the exchange rate is expressed as the number of Japanese Yen per US Dollar the spot and strike exchange rates in intrinsic value and call option formulae should be used as is. The option will only be exercised if the value of the US Dollar appreciates against the Japanese Yen or the Japanese Yen depreciates against the US Dollar in relation to the strike exchange rate.

Using the rates as is in the call option pricing formula without considering the logic behind the transaction or the appropriateness of the convention will result in an error. Simple application of max S T -K, 0 would result in a positive payoff which would be incorrect.

Logically, a rational buyer would not sell Japanese Yen buy US Dollar at a rate lower higher than the market rate. Convention wise, the exchange rates would need to be inverted first before application to the call option formula. If the exchange rate is expressed as the number of Japanese Yen per US Dollar, the rates will need to be inverted before application in the put formulae.

If the exchange rate is expressed as the number of US Dollar per Japanese Yen, the rates can be used as is. For a put option on USD see example 3: If the exchange rate is expressed as the number of Japanese Yen per US Dollar, the rates will need to be used as is in the put formulae. If the exchange rate is expressed as the number of US Dollar per Japanese Yen, the rates will need to be inverted before application in the formulae.

For an equivalent call option on JPY see example 4: If the exchange rate is expressed as the number of Japanese Yen per US Dollar, the rates will need to be inverted before application in the call formulae. Currency convention and risk free rates After determining the appropriate currency convention to use in the option pricing formula, another point of confusion is with regard to the risk free rates.

This is true for examples 1 and 3 below. When the currency convention is inverted in the call and put formula, i. Calculating option premiums After calculating the premium a common confusion is wrt the currency in which the premium is expressed. Total option contract value Following on point 3 above, another error lies in calculating the total contract value of the option. Putting in the values we have: Exotic Options Master Class: Options on shares, stocks, currencies and equities Master Class: Options and Derivatives Crash Course:

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