An underlying has a current price of $31. The premia on 3 month European put and call options on this underlying are $1 and $3 respectively. Both options have a strike price of $30. If the continuously compounded interest rate is 10%, is there an arbitrage opportunity here and, if so, how would you exploit it?
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An underlying has a current price of $31. The premia on 3 month European
put and call options on this underlying are $1 and $3 respectively. Both
options have a strike price of $30. If the continuously compounded interest
rate is 10%, is there an arbitrage opportunity here and, if so, how would you
exploit it? [Write no more than half of a page of A4]
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- An option has strike price of $9 and 12 months to expiry. The current price of the underlying share is $35 and its volatility (sigma) is 23%. The riskfree rate of interest is 4% per annum. Calculate d2 for this option. [your answer should have at least 2 decimal places]Use the Black-Scholes model to find the value for a European put option that has an exercise price of $62.00 and four months to expiration. The underlying stock is selling for $63.00 currently and pays an annual dividend of $1.92. The standard deviation of the stock’s returns is 0.21 and risk-free interest rate is 5.0%. (Round intermediary calculations to 4 decimal places. Round your final answer to 2 decimalConsider a European put and a European call option which are both written on a non-dividend paying stock, have the same strike price K = £80 and expire in T = 2 months. These options are trading for p = £21 and c = £30.80, respectively. The underlying stock price is S0 = £90. The continuously compounded risk-free rate of interest is r = 10% per annum. What is the present value of the arbitrage profit? Please explain your answer and show your workings. In your response, please show all cash flows (both today and at expiration) and explain why this is an arbitrage (i.e. risk-less) profit.
- ABC stock is currently trading at R70 per share. A dividend of R1 is expected after three monthsand another one of R1 after six months. A European call option on ABC stock has a strike priceof R65 and 8 months to maturity. Given that the risk-free rate is 10% and the volatility is 32%,compute the price of the option.Consider a 4-month forward contract for which the underlying asset is a stock index with value of 3, 825.97 and a continuous dividend yield of 0.5% Assume the continuous risk-free annual interest rate is 4.5%, a. Determine the no arbitrage forward price. $ Round your answer to the nearest cent b. Calculate the value of a long position if 2 month(s) later the index changes to 3, 825.97 and the risk-free rate is still 4.5% $ Round your answer to the nearest centJolly shares are currently trading at $135.43 and the standard deviation of Jolly's returns is 26%. The continuously compounding risk-free rate is 2%. Using the Black and Scholes pricing formula find the premium of a European put option with a strike price of $100 expiring one year from today. Answer to 2 decimal places.
- Suppose that a stock price is currently 35 dollars, and it is known that four months from now, the price will be either 51 dollars or 29 dollars. Find the value of a European call option on the stock that expires four months from now, and has a strike price of 39 dollars. Assume that no arbitrage opportunities exist and a risk-free interest rate of 10 percent.Answer =dollars.Use the following data for a fictitiously named company OPPS to answer the questions that follow: — The current stock price S is $23. — The time to maturity T is six months. — The continuously compounded, risk-free interest rate r is 5 percent per year. — European option prices are given in the following table: Strike Price Call Price Put Price K1 = $17.5 6.00 0.10 K2 = 20 4.00 0.50 K3 = 22.5 2.00 1.00 K4 = 25 1.00 2.50 You buy a call option with strike price K2 = 20 and sell a call option with strike price of K3 = 22.5. Then which of the following statements is INCORRECT? The derivative has zero-profit when the stock price at expiration is $21.5. You have set up a call spread. You have set up a bullish spread. The maximum loss is –$2 for a stock price at expiration less than or equal to $20. The maximum profit is $0.5 for a stock price at expiration greater than or equal to $22.5.What are the prices of a call option and a put option with the following characteristics? (Do not round intermediate calculations and round your answers to 2 decimal places, e.g., 32.16.) Stock price = $76 Exercise price = $75 Risk-free rate = 4.50% per year, compounded continuously Maturity = 4 months Standard deviation = 63% per year Call price $ Put price $
- The stock price of BellsNWhistles is currently trading at $120. Over each of the next two six-month periods it is expected to go up by 15% or down by 15%. The risk-free rate is 5% per annum with continuous compounding. There are no dividends due over the life of the option. Use the binomial model of option pricing to compute: (i) the price of a European call option with a strike price of €125. (ii) the price of an American call option with a strike price of €125. (iii) the price of a European put option with a strike price of €125. (iv) the price of an American put option with a strike price of €125.The market price of a one-year European call option is $9.243, written on a stock that is currently selling for $70. The stock is expected to go ex‑dividend in 6 months on a declared dividend of $5. The exercise price of the call is $80 and the current riskless rate of return is 3% per annum. What is the volatility (standard deviation) implied by the market price of this call option and an appropriate option pricing model allowing for dividends? Your answer should be within 2% of the correct solution (i.e., the correct σ ± .02).The current price of a non-dividend paying stock is $30. Use a two -step tree to value a European call option on the stock with a strike price of $32 that expires in 6 months. Each step is 3 months, the risk free rate is 8% per annum with continuous compounding. What is the option price when the volatility is 20%? (Hint: Calculate u and d using the CRR approach.) A. $1.48 B. $1.08 C. $1.68 D. $1.28