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Pricing Merger Risk as a Binary Payoff

Article Quant Q&A · Author: ababoua
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Summary

The document frames a merger-related investment as a contingent payoff: one amount if an acquisition succeeds and a loss if it fails. It explains that this payoff is not a standard call option, whose payoff depends on the asset price rising above a strike, but is closer to a binary claim tied to a discrete event.

If the stated event probabilities are risk-neutral, valuation follows from the discounted expected payoff. If they are subjective probabilities and the underlying event risk cannot be hedged through trading, those probabilities alone do not determine a unique market price; investor risk preferences also matter. The discussion is conceptual and gives no discount rate, hedge construction, or detailed risk analysis, so it does not provide a complete valuation model.

Key ideas

  • A payoff triggered by merger success or failure is closer to a binary claim than a conventional call.
  • Risk-neutral event probabilities allow valuation through the discounted expected payoff.
  • Subjective probabilities alone do not establish a unique price when the risk cannot be hedged.
  • Risk preferences matter when the contingent payoff is unhedgeable.

Tags

Event-drivenArbitrageOptionsRisk management
Full text
# Price of a risk arbitrage call


# Price of a risk arbitrage call












Let’s say I know that the probability of a merger-acquisition happening is p=1/4, the payoff i’d get in 6M (the time of the merger announcement) is 30. If the merger fails (q=1-p=3/4), my payoff is -10. What is the price of the call? And what are the risks involved and hedge?

## Answer by Ivan (score 1)

https://quant.stackexchange.com/a/38974

Your product is not a call, whose payoff would be of the form $Max(S-K,0)$, it is more like a binary option.

If your stated probabilities are (somehow) risk-neutral, then the price is simply the (discounted) expected value.

If -more likely- these are just subjective probabilities, and you cannot trade the underlying risk factor to hedge, then there is no unique price for this asset and your risk preferences need to enter the equation.

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.