For each of the following cases explain whether there exists an arbitrage opport

Question

For each of the following cases explain whether there exists an arbitrage opportunity or not. Assume that the holding costs are negligible and interest rates are continuously compounded. Quantify your answers.

(a) Spot price of gold is $1120/oz, and one-year-ahead gold futures are traded for $980/oz. Risk free interest rate is 10% per year.

(b) Spot price of gold is $1120/oz, and one-year-ahead gold futures are traded for $1120/oz. Risk free interest rate is 10% per year.

(c) Spot price of corn is $7.50/bushel, and six-month-ahead corn futures are traded for $6.20/bushel. Risk free interest rate is 8% per year.

(d) Spot price of corn is $7.50/bushel, and six-month-ahead corn futures are traded for $8.20/bushel. Risk free interest rate is 8% per year.

Explanation / Answer

a)theoretical Futureprice=1120*exp(0.1*1)=1237.79,since the theoretical price 1237.79 is not equal to the traded price of $980/oz ,therefore there is arbitrage opportunity.

b)theoretical Futureprice=1120*exp(0.1*1)=1237.79 ,since the theoretical price 1237.79 is not equal to the traded price of $1120/oz ,therefore there is arbitrage opportunity.

c)theoretical Futureprice=7.50*exp(0.08*0.5)=7.806 ,since the theoretical price 7.806 is not equal to the traded price of $6.20/bushel,therefore there is arbitrage opportunity.

c)theoretical Futureprice=7.50*exp(0.08*0.5)=7.806 ,since the theoretical price 7.806 is not equal to the traded price of $8.20/bushel,therefore there is arbitrage opportunity.

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