Description

This paper analyzes the problem of the balance sheet of an agent that invests in currencies different than those she finances. Assuming a constant rate of return and fixed financing costs, the agent can face the event of insolvency due to swings in the relevant exchange rate that is assumed to follow a geometric Brownian motion. Then, the process is generalized to allow dependency of the diffusion coefficient on the level of the exchange rate, reproducing many of the properties encountered in empirical studies of financial asset prices. The resulting hyperbolic process is calibrated via a martingale estimating function, and then we approximate the probability that the value of assets fails to match the value of liabilities at a given future date. The findings are consistent regardless the volatility assumption of the process. Finally, we give some insights to minimize the probability of such event.