Collared takeover exchange options with ratio barriers: practical extensions of the Haug–Haug knock-in/out Margrabe formula

Haug and Haug extend the Margrabe exchange option by adding knock-in and knock-out provisions written on the ratio of two asset prices. This paper applies and develops their framework for stock-for-stock takeover bids with collars. The analytical contribution is contract-specific: it combines the collar-induced exchange-option spread with the existing Haug–Haug ratio-barrier formulas, states the initial-state conditions under which those formulas apply, and extends the barrier representation to the binding lower-collar regime. In the standard collar case, the takeover bid is a capped exchange option, equal to a long lower-strike exchange option and a short higher-strike exchange option. When the walk-away provision is written on the same acquirer-to-target value ratio, each option leg can be valued using the Haug–Haug formula after a simple barrier transformation. When the lower collar binds above the exchange threshold, the payoff contains an additional target-share component contingent on the same barrier event; this component is valued as a closed-form asset-or-nothing ratio-barrier claim. Expanded numerical results document the interaction of the collar with down and up barriers, relative volatility, correlation, and time to completion, and clarify that the correlation effect is conditional on the sign of the spread’s net vega. The model provides a tractable benchmark for valuing collared merger consideration and for measuring the value impact of walk-away covenants.