1 Question 1 .Suppose the market price of a stock is So at time to. . The stock

Question

1 Question 1 .Suppose the market price of a stock is So at time to. . The stock does not pay dividends. . The interest rate is r >0 (a constant). . All the options below have strike K>0 and expiration time T> to. 1.1 European call .Assume that the value of the stock price is So >0.1 . Assume that the value of the strike price is K> 0.le"T-to). ·A European call trades today (time to) at a market price = So-0.1. . We formulate a trading strategy as follows: (a) buy the call, (b) short sell one share of stock, (c) save money in a bank. . The initial value of our portfolio is zero. . Find a scenario where this strategy leads to a profit Find a scenario where this strategy leads to a loss. . Note: if we do not exercise the option, we must buy back the stock, to cover the short sale. 1.2 American call . Assume that the value of the stock price is So >0.1 . Assume that the value of the strike price is K>0.le (T-to) ·An American call trades today (time to) at a market price = So-0.1 We formulate a trading strategy as follows: (a) buy the call, (b) short sell one share of stock, (c) save money in a bank. . The initial value of our portfolio is zero. Find a scenario where this strategy leads to a profit Find a scenario where this strategy leads to a loss. . Note: if we do not exercise the option, we must buy back the stock, to cover the short sale.

Explanation / Answer

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Basic terminology:

S0 = stock price as of now (Time zero = now, this day) > 0.1 > 10%

S T = Stock price at the expiry (After T months of Time;

Question = (Q)

X = Exercise Price = strike price = K is > 0

T > t0

Rate of Interest r > 0

Call Terminology:

C(S0, T, X) = Call Option valued at the price where the stock price being = S0, Time duration = T, exercise price = $X

Put notation:

P(S0, T, X) = Put Option valued at the price where the stock price being = S0, Time duration = T, exercise price = $X

American Call options are given an a suffix; while the European Call options are mentioned with an e suffix;

American Call notation:

Ca(S0, T, X) = Price of the American Call Option with the stock price of S0, in Time T, exercisable at $X

European Call notation:

Ce(S0, T, X) = Price of the European Call Option with the stock price of S0, in Time T, exercisable at $X

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Rationale or rule of the thumb as a general guideline:

When you expect that the stock prices are going to rise in the future then you can buy call options; and if stock prices are going to fall then buy put options;

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1.1 European Call:

1.2 American call:

1.3 European Put:

1.4 American Put:

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