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- 3. Leamington plc stock is currently trading at £9.20 and has volatility of returns of 30% per annum. Leamington plc is not expected to pay a dividend in the foreseeable future. The riskless rate is 3.5% per annum, continuously compounded. Consider a European call option on Leamington plc stock with strike price £9.00 and time to maturity three months. The risk-neutral probability of exercise for the European call option is * 0.1 3 0.2 8 0. 5 ܗ 0.5 5 0.6A one-month European put option on a non-dividend-paying stock is currently selling for $2.50. The stock price is $47, the strike price is $50, and the risk-free interest rate is 6% per annum. What opportunities, if any, are there for an arbitrageur? no opportunities; the put is fairly priced. an arbitrage strategy exists that could generate profit with a present value of at least $0.25. An arbitrageur should lend $49.50 for one month, buy the stock, and write the put option An arbitrageur should borrow $47.00 for one month, sell the stock, and write the put option6. Let us consider a European option on a stock that does not yield any dividend. Assume that that the price of this option is described by the Black-Scholes model with a drift of 10% per year, volatility of 40% per year. The current price of the stock is S, = £16. The risk-free interest rate on the market is 4% per year. 1) a) Calculate the price of a call option with strike price of £18 and a maturity T of one year. b) Using the put-call parity calculate the price of the corresponding put op- tion. 2) Imagine that in 6 months from now, the stock costs £16.4. Is it worth to wait 6 months before buying the call option above and investing in a saving account what we would have paid for buying the call at the initial time? Would this still apply if the stock costed £19.2 in 6 months from now?
- A 3-month European put option on a non-dividend-paying stock is currently selling for $3.80. The stock price is $48.0, the strike price is $51, and the risk-free interest rate is 6% per annum (continuous compounding). There is no arbitrage opportunity in this scenario. Is this true?The current price of a non-dividend-paying stock is $100. The risk free interest rate is 1% per year with continuous compounding. The implied volatility of a one-year at-the-money European vanilla call option is 0.2. (1). What should be the implied volatility of a one-year at-the-money European vanilla put? (2). Compute the price of the put. Express your result in terms of the standard normal cdf (e.g., if you get N(0.01), just keep N(0.01) in your answer.)Consider 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.
- 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.Consider a market where the assumptions behind the Black-Scholes model hold. A non-dividend paying share is currently priced at $300. A put option is available on the share with a strike price of $320 and one year to expiry. Volatility of 15% and the risk-free rate is 5% per annum. What would be the fair price of the put option.Suppose company B stock is last time traded at 68.23$, and our analysis shows that in one year from now, its price would either increase or decrease by 25%. (i.e. d=0.75, u=1.25) Assume that risk-free rate is 2.5% and the company pays no dividend in this time period. 4) What would be the payoff for a long position on European Call Option written on Company B equity, with time to maturity of 1 year, and strike price of 75$? Calculate the payoff for the up and down scenarios
- 2. The 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. The term structure is flat, with all risk-free interest rates being 10%. Calculate the price of a European put option that expires in six months and has a strike price of $30. PY of Dividends Dividend 1* e^(-12) + Dividend 2 * e^(-12)Suppose that a stock price is currently 61 dollars, and it is known that at the end of each of the next two six-month periods, the price will be either 18 percent higher or 18 percent lower than at the beginning of the period. Find the value of a European put option on the stock that expires a year from now, and has a strike price of 64 dollars. Assume that no arbitrage opportunities exist, and a risk-free interest rate of 10 percent.Suppose that Stock XYZ is currently trading at $50 and does not pay any dividends. Using a binomial tree with two periods, we would like to price a European call option with a strike of $50 and a maturity of six months. Assume that annual continuously compounded interest rate is 1% and the volatility of the stock is 30% per year. What is the value of q? 0.5565 0.4709 0.5000 0.3401 0.5000. You selected this answer.