Consider a one-period, two state case in which XYZ stock is trading at So=$35, h

Question

Consider a one-period, two state case in which XYZ stock is trading at So=$35, has u of 1.05and d of 1/1.05, and which the period risk-free rate is 2%.

Using the BOPM, determine the equilibrium price of an XYZ 35 European call option expiring at the end of the period.

Explain what an arbitrageur would do if the XYZ 3 European call was priced at $1.35. Show what arbitrageur’s cash flow would be at expiration when she closed.

Explain what an arbitrageur would do if the XYZ 35 European call was priced at $1.10. Show what arbitrageur’s cash flow would be at expiration when she closed.

Explanation / Answer

Probability of an upmove(p)=R-d/(u-d)=1.02-0.95238/(1.05-0.95238)=.69

Probability of downmove=1-.69=.31

Stock price in upmove=36.75

Stock price in downmove=33.33

Price of call option=1.75×.69/1.02=1.18

An arbitrageur will sell call option at $1.35

Thus arbitrage profit=0.17

An arbitrageur will buy call at 1.10

Thus arbitrage profit=1.18-1.10=.08

Thank you.

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