Abstract
The first goal of this paper is to clarify the implications of the no arbitrage assumption in the context of several countries and extend to a general setting of continuous-time finance and stochastic interest rates results which were more or less present in classical finance models such as the international APT (see Solnik (1983)). In particular, the remarkable relationship between the risk premia in two different countries and the sole volatility of the exchange rate is easily derived. Secondly, we examine the pricing and hedging of cross-currencies options when interest rates are stochastic in all countries. The dependence of risk neutrality arguments on the reference numéraire as developed in Geman (1989) becomes particularly clear in the case of several currencies.
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GEMAN, H., SOUVETON, R. No Arbitrage Between Economies and Correlation Risk Management. Computational Economics 10, 119–138 (1997). https://doi.org/10.1023/A:1008683928907
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DOI: https://doi.org/10.1023/A:1008683928907