The post-crisis market standard bootstrap of a risk-free rate for a foreign currency typically ensures that interest rate swaps in domestic and foreign currency, as well as cross currency swaps between the two currencies, trade at zero. Whereas the pre-crisis risk-free rate for the foreign currency, which is bootstrapped from only interest rate swaps in the foreign currency, is no longer used for discounting foreign future cash flows, it is still required for the computation of coupon payments resulting from a foreign currency floating rate bond. The present note points out that also for the pricing of an equity derivative based on a foreign currency stock it is reasonable to work with both the post-crisis and the pre-crisis risk-free rates. While the post-crisis risk-free rate is required to discount future cash flows from the derivative, the pre-crisis risk-free rate is required to model the drift of the stock price process. If the drift of the stock price process is (poorly) modeled using the post-crisis risk-free rate, the equity model is inconsistent with the cash market model. For example, it implies non-zero values for an equity forward contract.
On foreign currency equity drift rates
Newsletter