Find the risk neutral probability of state a

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Reference no: EM131243702

Call price as numeraire A stock that pays no dividends has current price S₀. In one year's time the stock price is 111 with probability 0.75 (state A), and 75 with probability 0.25 (state B). Annually compounded interest rates are 10%. The one-year 70-strike European call has price 10 at T = 0.

(a) Write down the payout of the 70-strike call at states A and B.

(b) By using a martingale condition for C₇₀(m, 1)/M_m, find the risk-neutral probability of state A with respect to the money market numeraire.

(d) Find the price of a one-year 80-strike American put. For K > 0, write down a simple formula for the price of the one-year K-strike American put.

(e) By using an appropriate martingale condition, show that q∗, the risk-neutral probability of state A with respect to the 70-strike call numeraire, satisfies

(f) Which of the following assets cannot be used as a numeraire in this binomial tree?

I. The stock.

II. The one-year 100-strike European call.

III. A forward contract with delivery price 90 and maturity one year.

IV. The ZCB with maturity T = 1.

V. The one-year 115-strike European put.

Reference no: EM131243702

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