# Bond Sweeteners

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## Abstract

Bond Sweeteners Riskcare 1 Background A company that is interested in financial expansion may acquire additional capital by issuing new company shares or bonds. To sweeten the bonds, often the company attaches embedded options that allow the bondholder to exchange the bond for shares. If, upon exercise of this embedded option, new shares are created, the option is called a warrant. Exercise of a warrant will therefore increase the total number of shares in the market. Note that the asset value per share may be less after exercise than before. We shall consider American-style warrants which may be exercised at any time. Consider the holder of such a warrant and suppose that upon exercise there is a dilution effect (the share price falls). Such a person could short sell shares immediately prior to exercising, then buy them back immediately after, thereby realising a risk-free profit (assuming the exercise is in some sense optimal). This represents an arbitrage opportunity and therefore cannot occur in a perfect market. (If it is "sub-optimal" to exercise, we shall show tht the share price moves against the exerciser, so eliminating the arbitrage possibility.) In order to understand this, we require a simple model for the total equity capital (assets - liabilities). We model the asset value, A, which is the total net assets excluding warrants, as a log-normally distributed random variable satisfying dAA = ud: + adX. (1) The total equity capital is A - NwW where Nw is the number of outstanding warrants and W is the price of a single warrant. This must be equal to the total value of all shares in the market, NsS, where N, is the number of shares in the market and S is the price of a single share: (2) Now, consider what happens if n warrants are exercised. The warrant liabilities fall to (Nw - n)W and A increases to A- + nK where K is the strike price of the warrant and A-is the value of A immediately prior to exercise. The number of shares jumps to N, + n. At all times, to avoid arbitrag

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