Consider the following options, which have the same two-year maturity and are written on the same stock. The firm does not pay dividends. Put option P1 has a strike price Xp1 = $50 Put option P2 has a strike price Xp2 = $100 Call option C1 has a strike price Xc1 = $100 Call option C2 has strike price Xc2 = $50 Your broker offers two trading strategies that can be derived from the options above. Strategy A: Long two puts P1 and long two calls C1 Strategy B: Long two calls C2 and long two puts P2 A. Which strategy would you choose if the two strategies have the same costs? Explain your answer. You now collect more information about the available securities. The stock has an implied volatility of 45% p.a.. The current risk-free rate is 1% p.a. The current stock price is $56. B. Calculate the value of the call option C1 using the Black-Scholes formula. Explain why such a deep out-of-the-money option still has a positive value/e: C. Calculate the cost of strategy B using the Black-Scholes formula.

Consider the following options, which have the same two-year maturity and are written on the same stock. The firm does not pay dividends. Put option P1 has a strike price Xp1 = $50 Put option P2 has a strike price Xp2 = $100 Call option C1 has a strike price Xc1 = $100 Call option C2 has strike price Xc2 = $50 Your broker offers two trading strategies that can be derived from the options above. Strategy A: Long two puts P1 and long two calls C1 Strategy B: Long two calls C2 and long two puts P2 A. Which strategy would you choose if the two strategies have the same costs? Explain your answer. You now collect more information about the available securities. The stock has an implied volatility of 45% p.a.. The current risk-free rate is 1% p.a. The current stock price is $56. B. Calculate the value of the call option C1 using the Black-Scholes formula. Explain why such a deep out-of-the-money option still has a positive value/e: C. Calculate the cost of strategy B using the Black-Scholes formula.

Essentials Of Investments

11th Edition

ISBN:9781260013924

Author:Bodie, Zvi, Kane, Alex, MARCUS, Alan J.

Publisher:Bodie, Zvi, Kane, Alex, MARCUS, Alan J.

Chapter1: Investments: Background And Issues

Section: Chapter Questions

Problem 1PS

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Consider the model of Black and Scholes. Consider the cash=or-nothing put option V (T) = 1{S(T)<= K} It pays out one unit of cash if the spot is below the strike at maturity. Evaluate the price of the option.
Multiple Choices: 1. What happens to a premium for a call option if the underlying futures price increases (all else equal)? (i) The premium increases. (ii) The premiums stays the same. (iii) The premium decreases. (iv) There is no relationship between the premium and futures prices. 2. What happens to a premium for a put option if volatility in the underlying futures contract decreases (all else equal)? (i) The premium increases. (ii) The premiums stays the same. (iii) The premium decreases. (iv) There is no relationship between the premium and volatility. 3. Which of the following is false about the seller an option? (i) The seller is required to have a margin account (ii) The seller has an obligation, not a right (iii) The seller always wants the futures price to rise (iv) The seller can choose to offset the option
Suppose the current ABC stock price is $50 and an option trader speculates this price will fall below $50 soon. Which set of actions is the best strategy for him? buy the Stock and write a $50 call buy $40 call and short $60 call short $40 put and buy $60 put buy $50 call and buy $50 put
You are pricing options with the following characteristics: •Current stock price (St): $35.60 •Exercise price (X): $50 •Time to expiration (T-t): 9 months •Risk-free rate (rf): 3.25% •Volatility (0): 45% (a): What is the Black-Scholes value of call option? In your hand-written solution, provide the calculations of d1,d2, and the final call price. Use Excel or another spreadsheet program to compute the values of N(d1) and N(d2). See the notes for details. (b): Using put-call parity, what is the value of a put option? For this case, assume continuous compounding, which implies that PVt(X)=e-r(T-t).X.
5. Explain and give appropriate use of the following option trading strategies along with their Payoff.: a. Spreads b. Straddles c. Strangles d. Covered Call and Protective Put. State Put-Call Parity theorem for European options. European put and call options with a strike price of Rs. 24 and expiry in 6-months are trading at Rs. 5.09 and Rs. 7.78, respectively. The current stock price is Rs. 20.37 with a risk-free interest rate continuously compounding equal to 7.48%. Is there an arbitrage opportunity? How can it be exploited?
am. 114.
Consider the following options on stock X: Option Delta Gamma Vega A 0.5 2.2 1.8 В 0.8 0.6 0.2 C -0.40 1.3 0.7 D 0.70 1.8 1.4 A bank is long 1000 units of Option A, short 200 units of Option B, short 2000 units of Option C, and short 500 units of Option D. The following two options are also available in the market: Option Delta Gamma Vega E 0.6 1.5 0.8 F 0.1 0.5 0.6 a) Design one strategy that would make the bank's portfolio delta neutral. b) Design one strategy that would make the bank's portfolio delta and gamma neutral. Explain why this strategy provides a better hedge with respect to changes in the price of stock X than the strategy you constructed in part (a). c) Design one strategy that would make the bank's portfolio delta, gamma, and vega neutral.
Short straddle is an option strategy that involves simultaneously selling a put and a call on the same stock with the same strike price, which is equal to the current stock price. Profit or Loss What is the purpose of this strategy? $400 SO 30 To profit from a large price increase SHORT STRADDLE A To profit from large price deviations from the current price D) To profit from a large price decrease 40 B To profit from the lack of price deviations from the current price 50 Stock Price at Expiration :
There are various ways to calculate the price of a call option using the Black-Scholes model. Below is a spreadsheet that breaks the required formulas into pieces to make it easy to work with. Column (1) shows the various inputs. The first five cells are the required inputs for a non-dividend paying stock. The remainder of the cells are the formula parts. Column (2) shows a solved problem for a stock selling for $50, with an exercise price of $45, an interest rate of 6 percent, 90 days (one-quarter of a year), and a standard deviation of .235. Column (3) shows how the cell values in Column (2) were calculated. Once you have this set up in the spreadsheet, you can calculate the price of any call option by substituting the correct values in the first five cells of column (2). Spreadsheet begins in row 2. Calculating a Call Price Using the Black-Scholes Model S 50 45 R 0.06 T 0.25 S 0.235 In(S/X) 0.105361 LN(B2/B3) r+0.50? 0.087613 B4+(,5)*(B6)^2 o(t)½ 0.1175 В6*((B5)^0.5) dl 1.083095…
Describe what a stock option is. what does it means to buy a "put" or a "call" and what you are expecting the stock to do for each (ie go up or down in price). Discuss when you would make money on a put option and when you would make money on a call option.
You hold a portfolio of an asset-or-nothing call and a cash-or-nothing put option written on a stock that does not pay dividends. The strike price of the options is the same. The payout of the cash-or- nothing option if it is exercised equals the strike price. Your portfolio is equivalent to O A plain-vanilla call option. O None of the other answers are correct. O A covered call position, i.e., a long stock + short plain vanilla call. O A plain-vanilla put option. O A protective put position, i.e., a long stock + long put option.
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