Consider a call option on stock XYZ with six months remaining to maturity. In a crisis, the volatility of the share increases and the share price drops. We should expect that: Multiple Choice О the value of the call option increases the value of the call option decreases it is uncertain if the value of the call option increases or decreases
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- In 1973, Fischer Black and Myron Scholes developed the Black-Scholes option pricing model (OPM). (1) What assumptions underlie the OPM? (2) Write out the three equations that constitute the model. (3) According to the OPM, what is the value of a call option with the following characteristics? Stock price = 27.00 Strike price = 25.00 Time to expiration = 6 months = 0.5 years Risk-free rate = 6.0% Stock return standard deviation = 0.49Which of the following positions in options benefit if the underlying stock price increases? Assume the options have several months remaining until the exercise date. a. Short position in call and long position in put b. Short position in both call and put c. Long position in a put d. Long position in call and short position in put e. Short position in a call f. Short position in a put g. Long position in a callYou sold a blue chip call option on Johnson and Johnson. Stock of JJ moves in the relationship with the Brownian motion - continuously without jumps, but volatility is not constant, but changes continuously (similarly to the stock price). Does hedging the option with futures contracts work, even if the stock market is closed over the weekend? Theta of the option is: Where q is dividend yield. Is the answer the same even if q is 0?
- Suppose that call options on ExxonMobil stock with time to expiration 6 months and strike price $87 are selling at an implied volatility of 27%. ExxonMobil stock price is $87 per share, and the risk-free rate is 6%. Required: If you believe the true volatility of the stock is 31%, would you want to buy or sell call options? Now you want to hedge your option position against changes in the stock price. How many shares of stock will you hold for each option contract purchased or sold?Suppose that call options on ExxonMobil stock with time to expiration 3 months and strike price $90 are selling at an implied volatility of 30%. ExxonMobil stock currently is $90 per share, and the risk-free rate is 4%.a. If you believe the true volatility of the stock is 32%, would you want to buy or sell call options?b. Now you need to hedge your option position against changes in the stock price. How many shares of stock will you hold for each option contract purchased or sold?Consider the following information for an individual stock Current share price is $30 Risk-free rate is 5% pa compounded continuously Volatility of the stock returns (σ) is 30% pa Strike price is $28 Time to maturity of the option is 12 months The firm is expected to pay no dividends over the next 1 year. Use the closed-form Black-Scholes model to price the European call option with the above characteristics 3.67 5.32 9.81 None of the above
- If a particular stock does not pay dividends and is currently priced at $24 per share, what should be the price of a call option with a maturity of one year and a strike price of $24.5 if put options with the same features currently cost $2? Assume a risk-free rate of 2%. (use 5 decimal places)A stock has an expected return of 14% based on its performance. Under the APT, given its risk exposure, the fair expected return is 18%. What would an arbitrageur trade in this situation? a. Buy the stock as price is too low. Buying increases price, reducing return. b. Buy the stock as price is too low. Buying increases price, increasing return. c. Do nothing - without risk free rate cannot tell. d. Short the stock as the price is too high. Selling reduces price, increasing returnLet the standard deviation of the continuously compounded return on the stock is 21 percent. Ignore dividends. Respond to the following. a) What is the theoretical fair value of the October 165 call? b) Based on your answer in part a, recommend a riskless strategy. c) If the stock price decreases by $1, how will the option position offset the loss on the stock
- Please show step by step work (not in excel): What is the call option premium given the following information? What would happen to the call price if the company initiated and paid a dividend before the expiration of the option? What would happen to the call premium if the expiration of the option expanded beyond the current 9 months? Stock price $36.00 Strike price $30.00 Volatility 16% Dividend Yield 0.00 Time 0.75 Riskfree Rate 2.70%is this statement TRUE or FALSE ? A stock with price 100 kr follows a one step Binomial model and will either increase invalue to 120 kr or decrease to 90 kr in one years time. The risk free interest rate is zero.An investor consider the increase and decrease in this model to be equally likely to happen.Is it true or false that the investor is risk-averse? is this statement TRUE or FALSE ?Please help solve in Excel. Suppose there is a stock that has a current price of $89.50. The risk free rate is 1%. There is an option with a price of $8.67 and a strike price of $85. This option will expire in 4 months. What is the implied volatility of this stock?