There is a European call option on the S&500 index. There are two months till maturity. The current value of the index is 3910 and the exercise price on the call is 3900. The continuously compounded risk-free interest rate is 5%. The volatility of the index is 20% per annum and the annual dividend yield is 3%. How much would you be willing to pay for this call option if each index point is worth $100?
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There is a European call option on the S&500 index. There are two months till maturity. The current value of the index is 3910 and the exercise price on the call is 3900. The continuously compounded risk-free interest rate is 5%. The volatility of the index is 20% per annum and the annual dividend yield is 3%. How much would you be willing to pay for this call option if each index point is worth $100?
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- Consider a European call option on the S&P 500 that is two months from maturity. The currentvalue of the index is 930, the exercise price is 900, the risk-free interest rate is 8% per annum,and the volatility of the index is 20% per annum. Dividend yields of 0.2% and 0.3% are expectedin the first month and the second month, respectively. Calculate the call priceThe stock price is currently $100. Over each of the next two six-month periods, it is expected to go up by 20% or down by 20%. The risk-free interest rate is 5% per annum with continuous compounding. What is the value of a one-year European call option with a strike price of $100? What is the value of a one-year European put option with a strike price of $100? Verify that the European call and European put prices satisfy put-call parity.A stock price is currently $100. Over each of the next two six-month periods it is expected to go up by 10% or down by 10%. The risk-free interest rate is 8% per annum with continuous compounding. What is the value of a one-year European call option with a strike price of $100? What is the value of a one-year European put option with a strike price of $100? Verify that the European call and European put prices satisfy put–call parity.
- A stock price is currently $100. Over each of the next two three-month periods it is expected to increase by 10% or fall by 10%. Consider a six-month European put option with a strike price of $95. The risk-free interest rate is 8% per annum, compounded continuously. What is the value of the option if it is American?A stock price is currently $ 100. Over the next two six-month periods it is expected to go up by 10% or go down by 10%. The risk-free interest rate is 8% per annum with continuous compounding. (i) What is the value of a one-year European call option with a strike price of $ 100. (ii) What is the value of a one-year European put option with a strike price of $ 100. (iii) Verify that the European call and the European put satisfy put-call parity.Consider a 2-year EUROPEAN PUT with a strike price of $65 on a stock whose current stock price is $60. Suppose that there are two time steps, and in each time step the stock price either moves up by 20% or moves down by 20%. Also suppose that risk-free rate is 5% per annum with continuous compounding . What is the value of the European put option?
- The current price of YBM stock S is $55. At-the-money European options with a strike price K = S and maturing in T = 6 months trade on YBM. The continuously compounded, risk-free interest rate r is 1.8 percent per year. If the call price is $5.22, then the no-arbitrage put price isConsider the futures contract written on the S&P 500 index and maturing in one year. The interest rate is 3%, and the future value of dividends expected to be paid over the next year is $35. The current index level is 2,000. Assume that you can short sell the S&P index.a. Suppose the expected rate of return on the market is 8%. What is the expected level of the index in one year?b. What is the theoretical no-arbitrage price for a 1-year futures contract on the S&P 500 stock index?c. Suppose the actual futures price is 2,012. Is there an arbitrage opportunity here? If so, how would you exploit it?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).
- A stock price is currently $50. Over each of the next two three-month periods it is expected to go up by 10% with a probability of 50% or down by 5% with a probability of 50%. The risk-free interest rate is 4% per annum with continuous compounding. What is the value of a six-month European call option with a strike price of $50? Use binomial tree method to solve this problemThe price of a European call that expires in six months and has a strike price of $30 is $2. The underlying stock price is $29, and a dividend of $0.50 is expected in two months and again in five months. Risk-free interest rates (all maturities) are 10% per annum with continuous compounding. What is the price of a European put option that expires in six months, and has a strike price of $30 and the same underlying asset?Suppose we have both a European call option and put option with an exercise price of $53 and the underlying stock is currently priced at $50. We are to note also that both options will expiry in six months. Further, market surveys suggest that the price of the stock can either go up by 20% or decrease by 25%. The current risk-free rate of interest is 2% per annum. (a) What is the expected price of the underlying asset at expiry date? (b) What is the value of the call option, using the binomial model? (c) If the put option is selling for $4.80, what should be the price of the call option to avoidarbitrage?