Consider the same parameterisation as in Question 1 but to be more specific, say the HJM processes

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Consider the same parameterisation as in Question 1 but to be more specific, say the HJM processes correspond to a Hull-White model with constant vol of 0.7% and mean reversion speed of 2%. Take lognormal spot FX vol as 15%. The correlation for the domestic-foreign rates is 30% and other correlations are 0%. Using the formula for forward vol in Section 10.1.1, determine how much of forward variance comes from the interest rates component and how much from the spot component for forward starting times 1y, 5y, 10y and expiries 1y, 5y,10y, 20y, 30y.


Question 1

Consider the following parameterisation based on Gaussian interest rates and lognormal spot FX : dSt = (rt – rƒt) Stdt + os(t) StdWS, dfa(t,T) = a(t, T)dt + od(t, T)dW? and dff(t,T) = f(t, T)dt + of(t, T)dW!, where dwddw! =quanto Libor rate, i.e. where the Libor rate LT (set at time T, with accrual fraction Ƭ  and paid at time T + Ƭ) is in the foreign currency but paid in the domestic currency without conversion at the FX rate.

Section 10.1.1

Df (t,T) Consider again the forward FX rate F(t, T) = St. As dis- cussed earlier, as expiry increases, the

We see then that the presence of stochastic interest rates will lead to higher forward variance if the

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