Decomposing a Double Knock-Out Payoff Versus Simulating the Underlying
Summary
The document compares two ways to value a structured payoff that rewards moderate upward or downward moves but expires worthless after a larger move. One method represents the payoff as an up-and-out call combined with a down-and-out put, then prices each component separately. The other simulates paths for the underlying and applies the complete payoff to each path, using a model calibrated to relevant market volatility data.
The discussion centers on whether separate component pricing, potentially with different volatility inputs or models, is less coherent than a single simulation framework. It raises the practical tension between fitting quoted prices for individual instruments and representing the joint payoff through one model. No valuation results or empirical comparison are provided, so the question remains open. The suitability of either method depends on how the components and barriers are defined, the available market quotes, and whether the pricing assumptions consistently capture the payoff's relevant risks.
Key ideas
- A structured payoff can sometimes be expressed as a combination of simpler barrier options.
- Separate pricing may use distinct volatility assumptions or models for each component.
- Path simulation values the combined payoff by applying its rules to simulated underlying paths.
- A simulation model may be calibrated to market volatility information relevant to the payoff.
- The document offers no numerical comparison, leaving model consistency and market fit as unresolved considerations.
Tags
Full text
# Valuation via decomposition or via simulation of the underlying? # Valuation via decomposition or via simulation of the underlying? My question might be very straight forward but I have seen both approaches being followed in practice so I am curious to see if there are arguments in favor or against each one. I am explaining my question via the following example. Let's say we want to value a twin-win double knock-out option on a single stock X (see payoff in the picture). Essentially at maturity if the underlying has moved up or down more than 10% we gain a return but if the movement is above 25% we gain nothing. This payoff can be easily decomposed into the sum of two options, an up-out call option with strike at 1.1/knock-out at 1.25 and a down-out put option with strike at 0.9/knock-out at 0.75. Approach 1: I value the options separately so i might use a Black-Scholes for each and add the results. That would mean that probably I would use a different implied vola for the two separate calculations. Approach 2: I simulate the underlying (via MC for example) and for each path I apply the payoff function below. For that I would need to make sure that I match the relevant parts of the vola surface so I would use maybe a local vol model. Question: People from big banks told me that that they always decompose such cases and value each component completely separately and sometimes using different models. I who do not work in a big bank :p , always used the second approach. As per my understanding the second approach is more appropriate because in such a way you can calibrate the model to the relevant products quoted in the market while with the second you have a quite different representation of the underlying (probably not matching the market quotes simultaneously) Am I missing something very basic here?
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.