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# Consider a European put option on a stock whose current price is \$52

INSTRUCTIONS TO CANDIDATES

(a) Compare Investopedia’s definition with the definition we gave in class. Show they are the same.

(b) Consider the “Box Spread Example” on the Investopedia webpage. For each stock price value at expiration listed below, state which options get exercised for or against the investor, what his payoff is for each of the options, and what his total profit is (ignoring commissions):

i. \$40

ii. \$52

iii. \$60

(c) Next read the article “1RONYMAN.doc” posted on Blackboard. Verify that his trades netted him \$287,500 up front and that he would owe \$250,000 at expiration if the options were European.

(d) As noted in the article, the options were American and not European. What was the potential (and ultimately realized) risk? How did this affect his “guaranteed” profit? Do a ‘back of the envelope’ calculation to estimate the underlying asset price when he made the trades–assume the risk-free rate is zero and use Put-Call parity to back out S. Is it surprising the calls he sold were exercised?

2. Consider a European put option on a stock whose current price is \$52 and has volatility 30%. The put expires in two months and has strike price \$55. The risk-free rate is 5%.

(a) Find the price of the put using a two-step binomial tree.

(b) Find the price of the put using the Black-Scholes formula.

(c) Repeat part (a) to find the price if the put option were American.

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