In this paper, we extend the Merton model of investment in discrete time to the cases when there is a finite number of investors and the market is with frictions represented by convex penalty functions defined for each investor. In the main result of this paper, we proved the existence of optimal strategy of investment by using a new approach based on the formulation of an equivalent general equilibrium economy model.

This study aims to identify the model that best approximates the credit spread that should be fixed on debt instruments issued by both public and private companies, considering the particularities of the Mexican market. Five models were analyzed: Merton's [1], those proposed by Denzler et al., the one presented in this paper, which includes the conformable derivatives, taking as a reference the change of variable made by Morales-Bañuelos et al., and the Corporate Default Risk Model (DRSK) for Publics Firms of Bloomberg [4]. The required financial information was obtained from the Bloomberg platform, from which the probabilities of default, credit spreads, and credit ratings for each company in the sample under the model (DRSK) were extracted directly. Likewise, the program developed by Moody's K.M.V. was used to obtain the EDF (Expected Default Frequencies). It was concluded that the Modified Merton model approximates to a greater extent the credit spreads that fix on a prime rate on the loans granted to the Mexican non-financial companies.

By reinterpreting the calibration of structural models, a reassessment of the importance of the input variables is undertaken. The analysis shows that volatility is the key parameter to any calibration exercise by several orders of magnitude. In order to maximize the sensitivity to volatility, a simple formulation of Merton’s model is proposed that employs deep out-of-the-money option implied volatilities. The methodology also eliminates the use of historic data to specify the default barrier thereby leading to a full risk neutral calibration. Subsequently, a new technique for identifying and hedging capital structure arbitrage opportunities is illustrated. The approach seeks to hedge the volatility risk, or vega, as opposed to the exposure from the underlying equity itself, or delta. The results question the efficacy of the common arbitrage strategy of only executing the delta hedge.

In this paper we focus on an implicit assumption in the BSM framework that limits the scope of market network connections to seeking gains in the currency basis, i.e., on trading strategies between the numeraire and the stock and between the numeraire and the option, separately. We relax this assumption and derive the equivalent of the standard BSM approach under a more general market network framework in order to assess its implications. In doing so, we find that it is not possible to hedge the implicit option that allows one to directly trade the option and stock. This represents a potential challenge to the BSM framework, since the missing market network connection provides a potentially useful mechanism for risk-bearing portfolio managers to alter their portfolios.