Stochastic Strikes in Asian, Barrier, and Compound Options
Summary
The document asks whether an option can have a strike that varies randomly over time and what such products are used for. The answers point to several related structures: an Asian option uses an average of the underlying over the contract period in its payoff; barrier options depend on whether the underlying crosses a threshold; and options on options add another layer of contingent value. These examples show that option payoffs can depend on a path or on other uncertain quantities, though they are not all simply a stochastic strike in the same sense.
The replies describe barrier features as a way to reduce option cost for hedging, particularly in currency or interest-rate settings, and mention compound options in project valuation where standard discounted cash flow may miss optionality. Another reply identifies the proposed payoff as a spread option with a potentially stochastic second asset. This is a short conceptual discussion, with no pricing methods, market examples, or implementation details; terminology and payoff structure need careful specification.
Key ideas
- Asian options use an average underlying price in defining the payoff threshold.
- Barrier options depend on whether the underlying crosses a specified level during the contract.
- Compound options provide an option on another option and can represent layered project uncertainty.
- A payoff subtracting one stochastic asset from another may be modeled as a spread option.
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Full text
# Options with a stochastic strike # Options with a stochastic strike Do options where the strike itself is a stochastic process exist? If they do - what are the motivations for such a product and where is it used ? Example: Call-Option with stochastic strike: $$(S_T(\omega) - K_T(\omega))^+$$ where $K_t$ is a stochastic process. $K_T$ could for example be of the form $K_T=f(X_T)$ where $f$ is a measurable function. ## Answer by jqotob (score 3) https://quant.stackexchange.com/a/10745 Asian options: strike is average of underlying over tenor. Underlying is stochastic. Options with kock-ins/knock-outs: Underlying is stochastic and may cross the kock threshold as it evolves. Option value depends on this cross or lack thereof (boolean). Options on Options, too. Motivations for Asian options you can google. Kock-ins and knock-outs lower the cost of an option so that a buyer who needs them for hedging purposes can more cheaply acquire downside protection. Generally applies to Currency/Interest Rate hedging. Options on options are more of a theoretical construct, although I'm sure they exist in practice. Generally useful for valuing complex projects with optionality when standard DCF approaches would not fully capture the stochasticity of the project's value. Dixit has a good chapter on this, I believe. ## Answer by airguru (score 1) https://quant.stackexchange.com/a/10778 I believe your example describes the payoff of a simple spread option. Some may argue that in reality this spread option has zero strike: $$ (S_T(\omega) - K_T(\omega)-0)^+ $$ Which leads us to the question: What exactly strike is anyway? Is it uniquely identifiable term in each payoff function? No It isn't.
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