In a previous article, we derived a sharp analytical lower bound for the price of a convertible bond. When a soft call covenant was present, a lower bound could only be derived in a simple credit-equity model, and two simplifying assumptions were made: (1) the soft call right may be executed at any time, starting at time t=0, and (2) the bond and its underlying equity are denominated in the same currency. This addendum summarizes the necessary adjustments to the formula in order to get rid of these restrictive assumptions.
Integrated convertibles - Investment styles and characteristics integration applied to convertible bonds
This article explores six investment styles like momentum, value, defensive and others in the niche asset class of US convertible bonds. While only carry and a characteristics integration approach yield promising results, it seems that both strategies can be explained by common equity and bond market factors. Thus, the case of characteristics investing in convertible bonds is not as strong as in other more traditional asset classes. However, convertible bond characteristics integration provides an interesting opportunity to get exposure to equity and bond markets as well as to multiple characteristics at once.
We discuss some critical aspects when evaluating convertible bonds whose underlying equity trades in a currency different from the bond currency.
The article studies the possibility for analytically approximating the price of a convertible bond within defaultable Markov diffusion models. Since convertible bond pricing requires time-consuming finite difference or tree pricing methods in general, such proxy formulas can help to calibrate model parameters more efficiently. The derivation is based on the idea to “Europeanize” the American conversion option of the holder. Consequently, the quality of the approximations stands and falls with the value of the early conversion premium, and the resulting formulas in general may be viewed as (often quite sharp) lower bounds for the price.
The equity forward with a given maturity is defined as today’s risk-neutral expectation of a stock price at maturity. If arbitrage-free prices for European put and call options with the given maturity are observed for different strike prices, the equity forward can be retrieved from the put-call parity. In particular, it is invariant with respect to different risk-neutral pricing measures which explain observed option prices, i.e. it is a model-free quantity. More precisely, the equity forward is given by the unique root of the (in practice partially) observed difference between calls and puts, viewed as a function in the strike price. In contrast, if only American-style put and call option prices are observed, the lack of a put-call parity makes it more difficult to retrieve the equity forward in an unambiguous way from the observed option data. In particular, the unique root of the difference between calls and puts in general is no longer equal to the equity forward. The present article investigates whether American-style put and call prices also determine the equity forward unambiguously. Unfortunately, this seemingly simple “yes or no”-question appears to be non-trivial and open, and the present investigation is not able to answer it.