USD-Notional GBPUSD Options and Forward Payoff Conversion
Summary
The document asks how to express payoffs for a GBPUSD European option with a knock-in feature and leverage when the contract notional is specified in USD. It describes an upside payoff when the terminal exchange rate exceeds the strike and a leveraged obligation to buy at the strike if the rate falls below a lower knock-in level. The central question is how USD notional should be converted into the GBP amount used in the payoff.
It also asks whether an FX forward payoff with the same USD notional should use the forward rate or strike rate as the conversion denominator. The author suggests dividing by the strike for the forward but is unsure whether the option should be treated the same way. The document supplies no resolved payoff formula, pricing method, or evidence, so it serves as a contract-denomination question rather than a completed valuation example. Correct treatment depends on which currency the payoff is settled in and how the contract defines notionals and currency exchange.
Key ideas
- The proposed GBPUSD option combines a call-like payoff with a leveraged knock-in obligation.
- The contract specifies notional in USD, while the payoff is expressed using the GBPUSD exchange rate.
- The document asks how to convert USD notional into GBP units for option and forward payoffs.
- No definitive conversion rule or Monte Carlo pricing solution is provided.
Tags
Full text
# What will be the payoff equation of a GBPUSD European Exotic option/FX forward with Notional in USD
# What will be the payoff equation of a GBPUSD European Exotic option/FX forward with Notional in USD
Given the currency pair , GBPUSD with
spot price as $S_t$ at time $t$, Strike price as $K$, $I$ is an indicator function indicating if GBPUSD is below the "Knock-in-Rate" at expiry, $L$ denotes the leveraged ratio and the spot price at time to maturity $T$ is $S_T$. Note that the knock-in-rate given is less than the strike rate.
If the Notional is given in USD, $Notional_{\scriptsize{USD}}$. Then how do you convert this into a GBP Notional for the payoff equation and what is the reason for this way of converting, i.e,
There are two conditions for the payoff:
- If spot at maturity is greater than the strike rate, then we have the option to buy GBPUSD at the given strike rate
- If the $S_{T}$ is lesser than the knock-in at maturity, then we are obliged to buy GBPUSD at strike rate with the leveraged Notional. Note that this will always produce a negative payoff since the given knock-in is lesser than strike.
$$ Payoff(t,T) = \frac{Notional_{\scriptsize{USD}}}{?}( ( S_T - K )^{+} - L.(K-S_{T} ).I) $$
I am basically trying to price this exotic FX option using Monte Carlo simulation and need to get the payoff right to get the correct price in the end.
Similarly If we go one step ahead and try creating a payoff for an FX forward at time $t$ of the same currency pair, where now K is the forward rate, would the payoff look like, $$ \frac{Notional_{\scriptsize{USD}}}{?} (S_{T}-K) $$ For FX forward, I reckon it will be $\frac{Notional_{\scriptsize{USD}}}{K}$, since notional exchange happens at the forward rate at maturity. However, should it not be the same or the FX Option where the currencies are bought or sold at the strike rate at maturity.Shown in full with attribution under the source's licence. Licence: CC BY-SA 4.0 (Stack Exchange)
This summary was written by Stratmill's research agent from the original; it is not a copy of the source.