FX Touch Option Valuation
A touch option is a transaction with one or two barriers. The buyer of the option will get a cash amount either if the barrier is touch or not touched. Touch options are becoming increasingly popular because they pay much higher yields compared to high/low options.
A touch option is the sort of option that promises a payout once the price of an underlying asset reaches or passes a predetermined level. Touch options allow investors to choose the target price, time to expiration, and the premium to be received when the target price is reached.
There are only two possible outcomes. If the barrier is broken a trader will receive the agreed full payout. If the barrier isn’t broken, the trader will lose the premium paid to the broker. Unlike vanilla calls and puts, touch options allow investors to profit from a simplified yes-or-no market forecast. Like regular call and put options, most touch option trades can be closed before expiration for a profit or a loss depending on how close the underlying market or asset is to the target price.
This type of option is popular with traders who believe the price of an underlying asset will pass a certain level in the future, and for those who aren’t sure whether the higher price level is a sustainable one. Speculative market participants like to use touch options as bets on a rising or falling exchange rate. Clients, who prefer to hedge, trade touch options as a rebate in order to secure themselves compensation in case their strategy doesn’t work out. Touch options are also often integrated into structured products to increase returns on forward and interest rates. They become especially useful during times of market volatility when prices might be uncertain.
An investor who chooses no touch option type is trading on the assumption that the price of their selected asset will fail to reach a specific level before the end of the expiry period. The investor may trade touch options, if he believes that the price of their selected asset will reach a specific level before the end of the expiry period. This presentation provides an introduction to FX touch options valuation.
Depending on the barrier types, the touch option can be divided into the following categories: one touch up/down; no touch up/down; double one touch; double no touch; one touch down no touch up; one touch up no touch down.
Barrier conditions for different types of touch options
No touch up: S_t<B
One touch up: S_t≥B
No touch down: S_t>B
One touch down: S_t≤B
Double no touch: 〖B_l<S〗_t<B_h
Double one touch: S_t≤B_l or S_t≥B_h
One touch down no touch up: S_t≤B_l or S_t<B_h
One touch up no touch down: S_t>B_l or S_t≥B_h where
B the barrier
B_l the low barrier B_h the high barrier
The payoff currency could be either the cash (base) or the asset (underlying).
payoff=Nominal×S×1_condition if the payout currency is asset payoff=Nominal×1_condition if the payout currency is cash
Valuation
Touch and no touch options are a great way for you to further customize your trading experience. Because there are only two different outcomes that can possibly occur, these are still considered to be binary options.
The present value of a one touch option is given by
where
S the spot exchange rate
σ the annualized volatility of the underlying rate
r the domestic interest rate between spot date and delivery date
rf the foreign interest rate between spot date and delivery date
Te the expiry date
Td the delivery date
ε 1 for a lower barrier, -1 for an upper barrier.
N(x) the standard normal cumulative distribution function
L the barrier level
R the domestic cash amount
w the rebate value
References: