A stock is priced at 85 and six-month European call and put options on the stock are available. A 90-strike call is priced at 5.40 and a 95-strike call is priced at 3.82. A 90- strike put is priced at 9.44 and a 95-strike put is priced at 12.74. A portfolio is comprised of 1 long 90 strike call, 1 short 95-strike call, 1 short 90-strike put, and 1 long 95-strike put. If the force of interest is 5%, calculate the payoff on this portfolio after 6 months if the stock price is 92 at that time.
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- A stock currently trades for $120 per share. Call options on the stock are available with a strike price of $125. The options expire in one month. The annualized risk free rate is 3%, and the expected volatility (annual) for the stock is 35%. Use the Black-Scholes option pricing model to calculate the price of the call option.The following prices are available for call and put options on a stock priced at $50. The risk-free rate is 6 percent and the volatility is 0.35. The March options have 90 days remaining and the June options have 180 days remaining. The Black-Scholes model was used to obtain the prices. Calls Puts Strike March June March June 45 6.84 8.41 1.18 2.09 50 3.82 5.58 3.08 4.13 55 1.89 3.54 6.08 6.93 Assume that each transaction consists of one contract (for 100 shares) unless otherwise indicated. What is the cost of the box spread if we are constructing a long box spread using the June 50 and 55 options? A. $76 B. $484 C. $2,018 D. $500A stock sells for $125. A call option on the stock has an exercise price of $110 and expires in 3 months. If the interest rate is 0.15 and the standard deviation of the stock’s return is 0.30. What would be the price of a put option on the same stock with an exercise price of $140 and the same time (3 months) until expiration? Show all workings. (See Appendix for the Cumulative Normal Distribution Table)
- The stocks of Cee Mobile Limited is currently trading at $73 each. The call option on thecompany’s stock has an exercise price of $70, with fifty (50) days remaining to expiration. It isassumed that the yield on treasury bills is currently 2%, while the volatility of the stock price isestimated as being 35%.Required:i. Using the Black-Scholes-Merton (BSM) model, calculate the value of the Call option, given theabove parameters. Show all relevant workings. ii. Of the value computed, how much is the intrinsic value and the time value of the Call option? iii. Using the BSM model and the information given above, calculate the value of the Put optionon the stock, with a similar strike price and days to expirationA stock sells for $125. A call option on the stock has an exercise price of $110 and expires in 3 months. If the interest rate is 0.15 and the standard deviation of the stock’s return is 0.30. What would be the price of a put option on the same stock with an exercise price of $140 and the same time (3 months) until expiration? Show all workings. (Please use the Cumulative Normal Distribution Table) (The current price of a stock is $33, and the annual risk-free rate is 6%. Acall option with a strike price of $32 and with 1 year until expiration has acurrent value of $6.56. What is the value of a put option written on the stockwith the same exercise price and expiration date as the call option?
- A stock is selling at INR 1,250. There exists a call option on this stock with expiry in 60 daysand an exercise price of INR 1,300. It is estimated that every 30 days, the stock price couldeither increase by 7% or decrease by 5%. The risk-free rate is 6%. Calculate the put price byusing the two-period binomial options pricing model.(Consider 360day-year)Which of the following call options on XYZ stock is most valuable? 1. Strike price = $ 40, 3 months to expiration 2. Strike price = $ 40, 3 months to expiration 3. Strike price = $ 50, 6 months to expiration 4. Strike price = $ 50, 6 months to expirationThe company’s stock price is $85 and will have a strike price of $90 in six months. The standard deviation is at 0.50 and risk-free rate is 5%. Determine the following: a. the value of the call option b. value of the put option c. put-call parity
- The current price of a stock is $50, and the annual riskfreerate is 5.5%. A call option with a strike price of $46 and 6 months untilexpiration has a current value of $9.59. What is the value of a put optionwritten on the stock with the same strike price and expiration date as thecall option?The stocks of Cee Mobile Limited is currently trading at $73 each. The call option on the company’s stock has an exercise price of $70, with fifty (50) days remaining to expiration. It is assumed that the yield on treasury bills is currently 2%, while the volatility of the stock price is estimated as being 35%. a. Using the Black-Scholes-Merton (BSM) model, calculate the value of the Call option, given the above parameters. Show all relevant workings. b. Of the value computed, how much is the intrinsic value and the time value of the Call option? c. Using the BSM model and the information given above, calculate the value of the Put option on the stock, with a similar strike price and days to expiration.A collar is established by buying a share of stock for $50, buying a 6-month put option with exercise price $45, and writing a 6-month call option with exercise price $55. On the basis of the volatility of the stock, you calculate that for a strike price of $45 and expiration of 6 months, N(d1) = .60, whereas for the exercise price of $55, N(d1) = .35.a. What will be the gain or loss on the collar if the stock price increases by $1?b. What happens to the delta of the portfolio if the stock price becomes very large?c. What happens to the delta of the portfolio if the stock price becomes very small?