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J 9
You are working on the options trading desk of FINM Investment Bank. Three-month European call and puts on stock BUSN with strike $60 are selling for $5 and $3, respectively. BUSN is currently trading at $60 and does not pay dividends. The interest rate is 3% p.a.c.c.
Are you able to make an immediate and riskless profit without any out-of-pocket expenses? If so, show all steps and calculations for the entire duration of your strategy.
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Solved in 2 steps
- Crisp Cookware’s common stock is expected to pay a dividend of $3 a share at the end of this year (D1 = $3.00); its beta is 0.8. The risk-free rate is 5.2%, and the market risk premium is 6%. The dividend is expected to grow at some constant rate g, and the stock currently sells for $40 a share. Assuming the market is in equilibrium, what does the market believe will be the stock’s price at the end of 3 years (i.e., what is )?National Grid PLC. (ticker: NGG) is currently trading at $59.11 per share. But youare bearish on the stock and believe that the price will fall to $56.32 in two weeks. Youdecide to short sell 100 shares. Your broker will charge 1.7% interest for lending shares toyou, independent of the length of the loan. You are required to pay the interest when youclose your short sale position. What is your expected investment outcome? A. $132.00 profitB. $178.51 profitC. $196.25 profitD. $210.00 profitE. $379.49 profit1. Suppose you had just gone long (purchased) on lot of Syarikat XYZ stock at a price of RM 15.00 each, for a total investment of RM 15,000. You believe this stock has long term potential but wish to protect yourself from any short-term downside movement in price. Suppose 3-month, at-the-money put options on Syarikat XYZ stocks are being quoted at RM 0.15 or 15 sen each or RM 150 per lot (RM 0.15 x 1,000). a. What would be the appropriate options strategy to hedge the long stock position? b. Show (in a table) the payoff to the combined position for a given range of stocks prices at options maturity in 3-months. c. Draw the payoff profile of combined positions.
- 1. Suppose you had just gone long (purchased) on lot of Syarikat XYZ stock at a price of RM 15.00 each, for a total investment of RM 15,000. You believe this stock has long term potential but wish to protect yourself from any short-term downside movement in price. Suppose 3-month, at-the-money put options on Syarikat XYZ stocks are being quoted at RM 0.15 or 15 sen each or RM 150 per lot (RM 0.15 x 1,000). a. What would be the appropriate options strategy to hedge the long stock position? explainb. Show (in a table) the payoff to the combined position for a given range of stocks prices at options maturity in 3-months. explainc. Draw the payoff profile of combined positions. explainQuestion 1 A bank has just sold a call option on 500,000 shares of a stock. The strike price is 40; the stock price is 40; the risk-free rate is 5%; the volatility is 30%; and the time to maturity is 3 months. a) What position should the company take in the stock for delta neutrality? b) Suppose that the bank does set up a delta neutral position as soon as the option has been sold and the stock price jumps to 42 within the first hour of trading. What trade is necessary to maintain delta neutrality? Explain whether the bank has gained or lost money in this situation. (You do not need to calculate the exact amount gained or lost.) c) Repeat part b) on the assumption that the stock jumps to 38 instead of 42. note: calculation should be provided with mathematical formularsQuestion 1 A bank has just sold a call option on 500,000 shares of a stock. The strike price is 40; the stock price is 40; the risk-free rate is 5%; the volatility is 30%; and the time to maturity is 3 months. a) What position should the company take in the stock for delta neutrality? b) Suppose that the bank does set up a delta neutral position as soon as the option has been sold and the stock price jumps to 42 within the first hour of trading. What trade is necessary to maintain delta neutrality? Explain whether the bank has gained or lost money in this situation. (You do not need to calculate the exact amount gained or lost.) c) Repeat part b) on the assumption that the stock jumps to 38 instead of 42.
- Ay 3. The price of a stock, which pays no dividends, is $76 and the strike price ofa10-month European put option on the stock is $90. The risk-free rate is 3.5%(continuously compounded). (1) Compute the lower bound for the option.(2) If the European put option price is $10, is there an arbitrage opportunity? How to takeadvantage of this arbitrage opportunity? What is the profit? (Please detail the actionsto be taken today and at the maturity of the option and include all the relatedcomputations)A trader bought ATM put for the strike price of 500@Rs. 19.72/- for Laurus Lab when stock was trading around 501 on spot. He also decides to add future (current month) at _. MIBOR rate is 4.65% & standard deviation is 36.79%. 1 lot = 2000. Calculate future price and find out profit & loss if at expiry stock closed at: a) 519 b) 607 c) 440 d) 392 Also draw the pay-off diagram highlighting the BEP and name the strategy opted by trader.Perform all calculations with excel: ABC Corporation is currently trading at $40, with volatility\ sigma 30%, r = 5%, and no dividends. Assume that the ABC stock price can be modeled according to a three period binomial approach with T = 9 months and n = 3, so that the stock price moves every 3 months. 1. Build out the binomial tree for ABC. 2. What is the value of an American put option with strike price 40? 3. What is the value of a European call option with strike price 50?
- Both a call and a put currently are traded on stock XYZ; both have strike prices of $50 and expirations of 6 months.a. What will be the profit to an investor who buys the call for $4.8 in the following scenarios for stock prices in 6 months? (i) $40; (ii) $45; (iii) $50; (iv) $55; (v) $60. (Leave no cells blank - be certain to enter "0" wherever required. Negative amounts should be indicated by a minus sign. Round your answers to 1 decimal place.) stock price profit i. $40 ii. $45 iii. $50 iv. $55 v. $60 b. What will be the profit to an investor who buys the put for $7.5 in the following scenarios for stock prices in 6 months? (i) $40; (ii) $45; (iii) $50; (iv) $55; (v) $60. (Leave no cells blank - be certain to enter "0" wherever required. Negative amounts should be indicated by a minus sign. Round your answers to 1 decimal place.) stock price profit i. $40 ii. $45 iii. $50 iv. $55 v. $60You are a trader for GreekLetters Ltd. You have sold 100,000 put options on a stock at strike $24.5 and also short 50,000 of the stock. The options expire in 9 months. The stock is currently trading at $24.09, and its volatility is estimated at 25% p.a.c.c. It pays a dividend of 2% p.a.c.c. The risk free rate of interest is 3% p.a.c.c and the option is currently selling for $0.70. How can you make your portfolio delta neutral?Consider a stock priced at $30 with a standard deviation of 0.3. The risk-free rate is 0.05. There are put and call options available at exercise prices of 30 and a time to expiration of six months. The calls are priced at $2.89 and the puts cost $2.15. There are no dividends on the stock and the options are European. Assume that all transactions consist of 100 shares or one contract (100 options). Suppose the investor constructed a protective put. At expiration the stock price is $27. What is the investor's profit?
