Kyoko Yagi

The pricing and optimal strategies of callable warrants

In this paper, we introduce a valuation model of callable warrants under a setting of the optimal stopping problem between the holder (investor) and the issuer (firm). A warrant is the right to purchase new shares at a predetermined price. When the new stocks are issued, the value of the stock is diluted. We consider the model taking the dilution into account. After identifying optimal policies for the issuer and the investor, we explore the analytical properties of the optimal exercise and call boundaries for the holder and the issuer, respectively. Furthermore, the value of such a callable warrant and the optimal critical prices are examined numerically using the binomial method.

THE VALUATION OF CALLABLE-PUTTABLE REVERSE CONVERTIBLE BONDS

Many companies issue some complex structured bonds. A reverse convertible bond is one of such structured bonds. In this paper we consider a valuation model of callable-puttable reverse convertible bonds which have the complex payoff in a setting of the optimal stopping problem between the issuer and the investor. Reverse convertible bonds issued by a company can be exchanged for the shares of another company. We analyze the pricing of reverse convertible bonds with call and put clauses and explore analytical properties of the value of the reverse convertible bond and optimal call and put boundaries by the issuer and the investor, respectively. Furthermore, we investigate how the call and put clauses affect the value and the optimal strategies for both of them.

The impact of convertible debt financing on investment timing

We develop a model to examine the timing of investment decisions in relation to the issuance of convertible debt by firms. Our model shows that when the demand shock has higher volatility, the firm finances the investment cost with high-coupon convertible debt. We find that default occurs earlier for firms that finance with convertible debt rather than with straight debt. We also find that firms with high-growth prospection, high volatility, and low capital costs that issue convertible debt tend to defer investments. Furthermore, we examine the investment decisions in which the convertible debt includes a call provision. We show that firms that use callable convertible debt invest earlier than those that use non-callable convertible debt by using suboptimal coupon payments. The opportunity from the forced conversion increases as the volatility increases. These results are consistent with recent empirical evidence.

The Valuation of Callable Financial Commodities with Two Stopping Boundaries

AbstractIn this paper we consider a model of valuing callable financial commodities which enable both an issuer and an investor to exercise their rights, respectively. We show that such a model can be formulated as a coupled stochastic game for the optimal stopping problem with two reflecting barriers. It is also shown that there exists a pair of optimal stopping rules and the value of the stochastic game. Most previous work concerning American options, Israeli options, convertible bonds and callable derivatives has required the specific payoff function when either of the issuer or the investor has exercise their option. However, we deal with a rather general payoff function of the underlying asset price and the time. We also explore some analytical properties of optimal stopping rules of the issuer and the investor.