Shout Options and Their Lock-In Payoffs
Summary
The document identifies the described contract as a shout option. A holder can lock in a value during the option’s life; at maturity, the payoff reflects the better of the locked-in value and the ordinary European option payoff. The question’s numerical example distinguishes the locked-in intrinsic value from the later asset-price increase and asks whether its proposed payoff interpretation is consistent.
The only answer names the contract but does not explain the formal payoff formula or resolve the apparent inconsistency in the example. The note is therefore useful for identifying the option type, but it offers little evidence or pricing guidance. Payoff details can depend on the specific contract terms, so the label alone does not settle how a particular shout feature is implemented.
Key ideas
- The described lock-in feature is identified as a shout option.
- The holder’s locked-in value may affect the payoff at maturity.
- The document raises ambiguity about how the locked-in value compares with the later call payoff.
- The brief answer names the option but does not derive its payoff formula.
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Full text
# What is the name and payoff of this exotic option (where the holder can lock in a price)?
# What is the name and payoff of this exotic option (where the holder can lock in a price)?
An exotic option is described as follows:
> Let $S_t$ be the underlying at $t$. The holder has the option to lock in the current price during the lifetime of the option, which he does for $S_{t}=50$. The strike price is $K=40$. At maturity, the option returns the payoff of a traditional European call or the intrinsic value at time $t$, whichever is greater. For example, if $S_T<50$ then the payoff is $10$. If $S_T>50$ then the payoff is the excess of the asset price over $50$.
I am quite confused, since by the description (if we ignore the last sentence) I understand the payoff to be simply the max of two calls: $\max(S_t-K,0)\textbf{1}_{S_T\le S_t}+\max(S_T-K,0)\textbf{1}_{S_T>S_s}$, where $\textbf{1}_{(\cdot)}$ is the indicator function.
After the last sentence, the payoff seems to be: $\max(\underbrace{S_t-K}_{=10},0) \textbf{1}_{S_T\le S_t} + \max(S_T-S_t,0) \textbf{1}_{S_T \gt S_t}$,
which is weird because e.g. for $S_T=55$ the payoff is $5$, i.e. less than $10$. If so, then the term "intrinsic value" refers to $S_T-S_t$ and not $S_t-K$.
Does this type of exotic option have a name? I tried searching "lock-in" option with no result so far. Is anyone familiar with what the text might be referring to and what the correct payoff is? Is there an error (contradiction) in the description?
## Answer by AlRacoon (score 9, accepted)
https://quant.stackexchange.com/a/70235
The option described is called a "Shout" option.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.