Restate the one step model for the fx rate

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Reference no: EM131243695

Binomial tree: FX forward brainteaser

Let X_t be 'cable', that is, the price at t in dollars of one pound sterling. At T = 0 there are two dollars per pound (so X₀ = $2.00). At T = 1, X₁ = $2.60 (state A) with probability 0.5, and $1.80 (state B) with probability 0.5. The one-year sterling interest rate r£ and one-year dollar rate r$ are 2% and 4% respectively, both annually compounded. Assume the accrual factor α = 1.

(a) Find ? such that a portfolio of one $2.00 call and ? pounds sterling has the same value in both states at T = 1. Hence prove that the price at T = 0 of the $2.00 call is

(b) Hence show that the risk-neutral probability (with respect to the dollar money market account) of state A is

(c) Restate the one-step model for the FX rate in terms of Y_t = 1/X_t, the value in pounds sterling of one dollar. By setting

find q∗, the risk-neutral probability of A with respect to the pound sterling money market account.

(d) Use q∗ to find by risk-neutral expectation the price of two £0.50 puts. Remember we are now working with a GBP asset so think of one dollar as a stock with price in pounds sterling. Is your answer the same as the price of the $2.00 call from (a)?

Reference no: EM131243695

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