NumericalExamplesOfPut-CallParityandMinimumValue

NumericalExamplesOfPut-CallParityandMinimumValue - Suppose...

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Numerical Examples of Put-Call Parity and Minimum Value 1 Notation: C Call price P Put price S Stock price E Exercise price r Continuously compounded interest rate t Time to expiration We assume throughout that the stock pays no dividends. 1. Put-call parity is a relation between the price of a put, the price of a call, and the stock price. It holds both at expiration and prior to expiration. Put-call parity states that C = S - Ee - rt + P (1) Assume S = $110, E = $100, r = 0, t = anything (because r = 0). Then (1) implies C = $110 - $100 + P . Therefore: If P = $2, then C = $12 If P = $5 then C = $15. 2. A second option-pricing formula relates the price of a call to the stock price and the present value of the exercise price. C max(0 , S - Ee - rt ) . Like put-call parity, this relationship holds at or before expiration. The minimum value is greater than the intrinsic value max(0 , S - E ). 1 Notes for Finance 100 (sections 301 and 302) prepared by Jessica A. Wachter.
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Unformatted text preview: Suppose that S = $101, E = $100, r = . 06, t = 1. Then C ≥ max(0 , 101-94 . 18) = 6 . 82 . Note: $5.82 of the $6.82 minimum value comes from the time value of money, and $1.00 comes from the intrinsic value. Question : Can the minimum value be used to show why you would never exercise an American call option on a non-dividend paying stock prior to expiration? Both put-call parity, and the minimum value of a call are arbitrage relations, in the sense that if they do not hold, it is possible to construct a strategy that makes positive gains and has no possibility of losing money. If such a strategy were to exist, traders would exploit it immediately, and the relations would be restored....
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NumericalExamplesOfPut-CallParityandMinimumValue - Suppose...

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