Payoff Profiles
- 03:25
Understand how the payoff of an FX option works, and which currency it naturally occurs in.
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Transcript
When thinking about the payoff of an option, we are calculating what the positive value is to the buyer if the option is exercised. With stock options, if I own a 100 call on stock A, B, C, and the stock finishes at 110, my payoff is $10 per share.
With FX options, the payoff of an option naturally occurs in the quoted currency, so sticking with our euro dollar example from before, if we buy a euro call and the spot rate finishes above the strike, then our positive payoff will be measured in dollars. An example of this is coming up next.
If we want to calculate our payoff in the base currency, then we can simply divide by the prevailing spot FX rate on expiry. to get the amount.
Here we see the payoff of a 1.10 Euro dollar call option versus the terminal spot FX rate. Note that the payoff in the quoted currency dollars is linear, and when positive moves 1 for 1 with the underlying. The example illustrated here considers a spot FX finish at 1.20. In which case we would exercise our euro call, buy euros at 1.10, and simultaneously sell them back into the market at 1.20. For a fixed amount of euros, we would get a payoff of $0.10 per Euro.
If we want to see the payoff in the base currency instead, then we need to divide our quoted currency payoff by the prevailing spot rate at expiry. This will produce a non-linear payoff as the spot rate on expiry is driving both the quoted currency payoff and the divisors.
This may seem odd, but that is only because it is peculiar to be able to switch between the two sides of the price. In our case, euros and dollars. Options are normally the right to buy an asset, say a stock at a certain price in dollars. The payoff is linear in dollars, but what if we wanted our payoff to be in shares instead? In order to do that, we would need to convert our dollar cash payoff into shares by buying shares at the prevailing market price. This would then match the non-linear payoff we see in euros above. It would be odd to talk about the payoff of a stock option in shares, but because in FX our asset is just another currency, we can talk in these terms if we wish. It's however more conventional and simpler to talk and think of a linear payoff in the quoted currency.