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In this chapter we concentrate at the most popular model for convertible bond (CB) valuation in a one-factor, stochastic underlying stock price setting. Through the last decade, the Tsiveriotis–Fernandes model (1998) has become a widely commented model that involves the state of default of the issuer of the CB. A routine approach to the solution of this model is the usage of methods of finite difference schemes (FDS). However, for many people trained in finance these methods are not very intuitive and they tend to ignore them and prefer to use binomial-tree approach as more intuitive technique. For that reason, our primary focus is to highlight the answer of the so far unanswered question: Does the binomial-tree approach to CBs provide accurate pricing, hedging, and risk assessment? We show on a set of representative examples that by using binomial-tree methodology one is unable to provide a consistent analysis of the pricing, hedging, and risk assessment. We start the chapter with the basics of CBs and CB market. We then explain the implementation of TF model within binary-tree approach. We conclude the chapter with performance valuation of binomial-tree approach showing unexpected behavior in practice areas such as pricing (profile of CB's price versus underlying stock price), hedging (performance of CB's delta, gamma, and convertible arbitrage strategy versus underlying stock), and risk assessment (Monte Carlo VaR with respect to the underlying).

This chapter extends Panyagometh and Roberts (2008) by taking into account differences in costs of closure among countries and the effects of subordinated debt on moral hazard problems. Our results show that a mandatory subordinated debt policy (MSDP) can be used with contingent purchase and assumption policy to further reduce probability of future bank failure if the high level of uninsured debt can improve the effectiveness of monitoring. While a MSDP might be appropriate for some developed countries with effective informational and supervisory environments and developed financial markets, such as the U.S., extending a MSDP into developing countries is questionable.

Using a two bank, two-period game-theoretic model, this chapter shows that contingent purchase and assumption policy under which the choice of acquirer for a failed bank is contingent on the surviving banks’ risk-taking behavior is generally most effective in reducing moral hazard problems, particularly for countries with low levels of competition and high regulatory barriers. Moreover, we find that to minimize the probability of future bank failures, the choice of acquiring bank should be based not only on the short-term goal of resolving the insolvencies of financial institutions, but also on the long-term effects of ex ante risk-taking incentives.

The mathematical models used to describe the dynamical behaviour of a group of closely-spaced road vehicles travelling in a single lane without overtaking are known as car-following models. This paper presents a novel car-following model, which differs from the traditional models by having an equilibrium solution that corresponds to consecutive vehicles having not only zero relative velocity, but also travelling at a certain desired distance apart. This new model is investigated using both numerical and analytical techniques. For many parameter values the equilibrium solution is stable to a periodic perturbation but, for certain parameter values, chaotic motion results. This shows that in congested traffic, even drivers attempting to follow a safe driving strategy, may find themselves driving in an unpredictable fashion.

The credit migration process contains important information about the dynamics of a firm's credit quality, therefore, it has a significant impact on its relevant credit derivatives. We present a jump diffusion approach to model the credit rating transitions which leads to a partial integro-differential equation (PIDE) formulation, with defaults and rating changes characterized by barrier crossings. Efficient and reliable numerical solutions are developed for the variable coefficient equation that result in good agreement with historical and market data, across all credit ratings. A simple adjustment in the credit index drift converts the model to be used in the risk-neutral setting, which makes it a valuable tool in credit derivative pricing.

Estimating parameters of constrained optimization models in a consistent way requires a different set of methods than what is available in a typical econometric toolkit. We identify three complications likely to arise in this context, and suggest solutions to those complications: (i) the bi-level programming character, (ii) ill-posedness, and (iii) derivation of estimator properties. The solutions suggested involve a combination of numerical techniques and utilization of out-of-sample information through Bayesian techniques. The proposed framework is also suitable for typical empirical problems arising in trade analysis such as the estimation of trade equilibrium models and data balancing exercises.