Question

Dorothy Santosuosso does a lot of investing in the stock market and is a frequent user of​ stock-index options. She is convinced that the market is about to undergo a broad retreat and has decided to buy a put option on the​ S&P 100 Index. The put carries a strike price of 906 and is quoted in the financial press at $14.51. Although the​ S&P Index of 100 stocks is currently at 900.43​, Dorothy thinks it will drop to 851 by the expiration date on the option. How much profit will she​ make, and what will be her holding period return if she is​ right? How much will she lose if the​ S&P 100 goes up​ (rather than​ down) by 25 points and reaches 925 by the date of​ expiration?

A stock trades for ​$44 per share. A call option on that stock has a strike price of ​$52 and an expiration date six months in the future. The volatility of the​ stock's returns is 47​%, and the​ risk-free rate is 6​%. What is the Black and Scholes value of this​ option?

Answer 1

1a. Profit and Holding period return if price on expiry is $851

Profit = Strike price - Spot price at maturity - Premium paid

Profit = 906 - 851 - 14.51

Profit = $40.49

Total Profit of 100 Stocks = $4049

Holding Period Return = Profit / Premium paid = $40.49 / 14.51 = 279.05%

1b. if the spot price at maturity is at 925, the put option will not be exercised and the amount lost is equal to premium paid = $14.51 and total loss on 100 Stocks = $1451

2. Value of Call = $3.52

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