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    Put-Call Parity, Options and Arbitrage

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    Question 1
    What is put-call parity and why does it hold? Please show your proof?

    Question 2
    The following prices are observed. How are you going to profit from the opportunity?

    Stock A is selling for $95.00
    Call options on stock A with exercise price of 90 and with April expiration are selling for $9 per share
    Put options on stock A with exercise price of 90 and with April expiration are selling at $2.5 per share
    At the current t-bill rate, $89 invested today will grow to 90 at the option's maturity date.

    Question 3
    The following prices are observed. Use an arbitrage strategy to get an arbitrage profit.

    Stock A is selling for $95.
    Call options on stock A with an exercise price of 85 is selling for $12 per share
    Call options on stock A with an exercise price of 90 is selling for $10 per share
    Put options on stock A with an exercise price of 85 is selling for $1.25 per share
    Put options on stock A with an exercise price of 90 is selling for $1.75 per share
    At the current t-bill rate, $89 invested today will grow to 90 at the option's maturity date and 84.06 invested today will grow to 85 at the option's maturity date.

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    https://brainmass.com/business/options/put-call-parity-options-arbitrage-378166

    Solution Preview

    Please see responses below.

    Question 1
    What is put-call parity and why does it hold? Please show your proof?

    Put-call parity is a relationship between the prices of call options and put options, when both options have the same expiration date and the same strike price.

    Assume a put, a call, the underlying stock, and a riskless bond are all available, and that the put, call, and bond all have the same maturity. Then at each time until maturity, the relationship is

    C + KB = P + S,

    where

    C = call price
    K = option strike price
    B = price of riskless bond which pays 1 at maturity
    P = put price
    S = stock price.

    Proof: Let F be the stock price at the maturity date. If you hold a call option and K bonds today, then at maturity your holdings are worth K if F <= K. This is because your K bonds will be worth 1 each (total of K), and your call option will be worth 0. If on the other hand F > K, your holdings will be worth F, because the bonds will be worth K and the call will be worth F - K.

    If you ...

    Solution Summary

    The solution discusses the put-call parity, options and arbitrage.

    $2.19

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