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A stock that does not pay dividend is trading at $73.1. A riskless bond that will...

A stock that does not pay dividend is trading at $73.1. A riskless bond that will pay $100 after a year is trading at $97. A European call option on the stock with strike price of $64 and one year to maturity is trading at $5.8. Propose an arbitrage strategy and prove that it is an arbitrage strategy.

Expert Solution

Given Information

Current Stock Price $73.10

European Call Option Strike Price after 1 year $64.00

Price of call option $5.80

Price of Risk less bond $97.00

Maturity Value of Bond after 1 year $100.00

Developing an Arbitrage strategy

Short sell share - buy a call option - Invest in bond - Redeem maturity value of bond after 1 year - Exercise call option and buy a share / directly buy a share - Square off short selling position

Explanation

1. Short Sell 970 shares and get cash $70,907.00

2. Buy 970 call options with cash from sale proceeds $-5,626.00

Net cash in hand $65,281.00

3. Invest net cash in hand in bonds and get bond units 673 Units

4. Redeem bond units after 1 year (673*100$) $67,300.00

5. Buy a share after 1 year and close short position

If price after 1 year is >64$ exercise call option (970*64) $62,080.00

If price after 1 year is <64$ Buy share from market which obviously costs less

Therefore, maximum price paid is 62080$

Minimum guaranteed Net Proceeds in hand after 1 year (67300-62080) $5,220.00

Arbitrage strategies ensure guaranteed profits without risk. Since 5,220$ is a guaranteed profit without risk. This is an arbitrage strategy.

*Assumption: Commission for short selling shall be less than 5220$. Moreover, no short selling fee is not given in question, hence this strategy is effective

jeff jeffy answered 1 year ago

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