Exercise 2.10 Suppose that a stock traded in France satisfies the stochastic differential equation dS(t) = 0.04S(t)dt + 0.15S(t)dW(t), while the EUR/CAD’s exchange rate process satisfies dC(t) = 0.025C(t)dt+ 0.40C(t)dZ(t).

The correlation between the Brownian motions W and Z is 0.65. The annual risk-free rate in France and Canada are respectively 4% and 2%, and the 1-
year forward contract on EUR/CAD is $1.34. The spot exchange rate c0 on EUR/CAD is determined by the covered interest rate parity formula:
F = c0erEUR−rCAD.
We want to price a European put on the asset S paying off in CAD.

(a) Why would an investor buy a quanto call or a quanto put paying off in the domestic currency?

(b) Write the expressions of ¯ σ1 2, ¯ σ2 2, and σ2, and compute their values.

(c) Write the expression of the value of the put P(t, S0, c0), including the values of D1 and D2.

(d) What is the exchange rate c0 today?

(e) Today, S = $27. Compute the value of a 3-month maturity put if the strike price is $28.