Three essays on the pricing of convertible bonds and on put-call parities

This thesis is a collection of three papers that have the valuation of derivative securities as a common theme. The first paper empirically compares three convertible bond valuation models. We use an innovative approach where all model parameters are estimated by the Marquardt (1963) algorithm using a subsample of convertible bond prices. The model parameters are then used for out-of-sample forecasts of convertible bond prices. The mean absolute deviation, which is calculated as the absolute difference between the model and the market price and expressed as a percentage of the market price, is 1.70% for the Ayache-Forsyth-Vetzal (2003) model, 1.74% for the Tsiveriotis-Fernandes (1998) model, and 2.12% for the Brennan-Schwartz (1980) model. For this and other measures of fit, the Ayache-Forsyth-Vetzal and the Tsiveriotis-Fernandes models outperform the Brennan-Schwartz model. The second paper examines the market memory effect in convertible bond markets. More specifically, we look at the pricing of convertible bonds issued after the original issuer adversely redeemed previous issues without giving an opportunity for investors to benefit from bond value appreciation. We find evidence that the market underprices new convertible bond issues of firms that call their bonds early. We also find that the degree of market underpricing depends on whether the convertibles are more debt- or equity-like. In the third paper, the European put-call parity condition is used to estimate the early exercise premium for American currency options traded on the Philadelphia Stock Exchange. Using a sample of 331 pairs of call and put options with the same exercise price and time to expiration, we find that the early exercise premium on average is 5.03% for put options and 4.60% for call options. The premia for both call and put options are strongly related to the interest rate differential and time to expiration. These results are important to consider when valuing American currency options using European option pricing models.