Optimal exercise strategies for corporate warrants

Abstract

In this paper, we analyse the optimal exercise strategies for corporate warrants issued by levered firms. For the analysis, we distinguish between two exercise variants, namely the traditional block exercise and competitive exercise in equilibrium. We find that the optimal exercise date under the block condition can be before or after an optimal exercise in equilibrium. Surprisingly, optimal block exercise can occur even without any dividend payments in contrast to the competitive exercise. As a consequence, the asset values and the stock volatility under block exercise fundamentally deviate from those under the competitive exercise variant. Moreover, the value of a warrant in the block case and its exercise strategy do not coincide with those of a corresponding call option which contrasts with the assumption of 'option-like' warrant valuation.Warrants, Exercise strategy, Option pricing, Financial structure,

A Reduced-Form Model for Warrant Valuation

“…More recently, Linder and Trautmann (2009) provide sufficient conditions for sequential exercise not to be optimal. If warrant holders are price takers, Constantinides (1984) and Koziol (2006) show that there exist Nash equilibrium where price takers will exercise warrants as a block, although the price will be less than or equal to that of a large trader. In these models, the results depend critically on both the use of the cash proceeds by the firm and the specific liability structure assumed.…”

Pricing Multiple Stock Warrants with Strategic Exercise

“…K comes from equating the assets and liabilities of the firm. At each node k , we must have the asset liability identity: (10) Where N is the number of shares outstanding and i K is the number of warrants of type i that were issued.…”

“…Articles on warrant valuation which rely on the reasonableness of block exercise include Ingersoll (1977), Brennan andSchwartz(1977, 1980), Schulz and Trautmann(1994), and Crouhy and Galai(1994). examines exercise strategies for warrants in a competitive market [16]. Kapadia and Willette(2005) analyze exercise strategies for Europeantype warrants in large trader economies when large trader hold the same number of warrants while Linder and Trautmann(2006) consider the more general case of large traders with a competitive fringe [15].…”

Impact of Imperfect Information on the Optimal Exercise Strategy for Warrants

“…one particular warrant holder cannot affect the aggregate exercise volume f · m with his or her individual decision. This form of competition among warrant holders is also considered by Constantinides (1984) and Koziol (2006a).…”

“…Remarkably, if a partial exercise takes place, the exercise volume declines with the signal v . This relationship is surprising because typically the optimal exercise volume increases with a more favourable firm value (see, for example Koziol, 2006a). The intuition for this outcome is that in this equilibrium the warrant holders – as explained above – suffer from a lower aggregate exercise volume and benefit from a more favourable signal v .…”