: Today is time t = 0, the current value of the underlying is S = £10.00, and the risk-free interest rate is r = 0.05 per annum. Today it is possi- ble to buy a European vanilla call option with exercise price E = £8.00 and expiry date T = 6 months for C = 275 pence. What is the fair value in pence for the corresponding European vanilla put?
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- The price of a European CALL option is $8.00 and a European PUT is $10.00. The expiration date is 1 year and has an exercise price k=$60.00, the share price of the underlying asset is quoted today at $60.00. The risk-free rate is 10% per year. Propose a strategy that generates arbitrage and a profit.You are considering a European put option and a European call option on ABC Ltd and have available the following information. The put option with an exercise price of $15 and time to maturity of 60 days is priced at $2.00. The call option with the same exercise price and time to maturity is priced at $3.00. The underlying asset price is $15. The risk-free rate is 2% per 60 days. Could an arbitrage profit be earned? If so, how much the arbitrage profit is? Show your works (Hint: use discrete put-call parity equation and consider two scenarios for stock price at maturity of the options: $10 or $20).Consider a one-period binomial model in which the underlying is at 65 Euros, and can go up 30% or down 22% each period. The risk-free rate is 8%. Determine the price of a European put option with exercise price of 70. Assume that the put is selling for 9 Euros. Demonstrate how to execute an arbitrage transaction and calculate the rate of return. Use 10000 puts.
- Consider a European call option and a European put option that have the same underlying stock, the same strike price K = 40, and the same expiration date 6 months from now. The current stock price is $45. a) Suppose the annualized risk-free rate r = 2%, what is the difference between the call premium and the put premium implied by no-arbitrage? b) Suppose the annualized risk-free borrowing rate = 4%, and the annualized risk-free lending rate = 2%. Find the maximum and minimum difference between the call premium and the put premium, i.e., C − P such that there is no arbitrage opportunities.D3)Consider a European call option struck "at-the-money", meaning the strike price equals current stock price. There is one year until expiration and the risk-free annual interest rate is r = 0.06. We define the call option's "delta" as aCE(S,t) A as Is it possible to determine whether or not the call option's delta is greater than or less than 0.5?
- Suppose the European call and put options with strike price $20 and maturity date in 1 month cost $2.0 and $1.0, respectively. The underlying stock price is $18 and the risk-free continuously compounded interest rate is 8%. (a) Is there an arbitrage opportunity? (b)If yes, how would you implement arbitrage opportunity?Consider a European call option on DELL that has an exercise price of $100 and four months (14%) until expiration. The annual risk-free rate of interest is 0.07%, compounded continuously. DELL call option and stock are priced at $5.79 and $97.80 per share, respectively, today. (a) Compute today’s value of a European put option on DELL that has the same exercise price and expiration date as the above call option on DELL. Show numerically which option has a higher time value of option. (b) Compute the profit to the writer of the in/at/out of (circle one) money put option if DELL stock is priced at $95.0 when the option expires. (c) Suppose that DELL has 10 million shares of common stock outstanding, and issues one million warrants that each can be exchanged for 2 shares of common stock. The warrant has the same exercise price and expiration date as the above call option on DELL. (i) Compute the value of each warrant that is in/at/out of (circle one) money. (ii) If you currently own 1,000…Consider a one-period binomial model in which the underlying is at 65 Euros, and can go up 30% or down 22% each period. The risk-free rate is 8%. European Put Option with Execution Price of 70 Euros. Assume that the put is selling for 9 Euros. Demonstrate how to execute an arbitrage transaction and calculate the rate of return. Use 10000 puts.
- A European-style put option that expires two periods from now has an exercise price of $125. The per-period risk-free rate in the economy is 5.4%. The underlying asset currently sells for $107.50 and will either go up in value by 12% or down by 10%. How much should the put option sell for right now? Round your answer to the nearest penny.What is the price of a European CALL option that is expected to pay a dividend of $2 in three months with the following parameters? s0 = $40d = $2 in 3 monthsk = $42 r = 10%sigma = 20%T = 0.5 years (required precision 0.01 +/- 0.01)The price of one-year and two-year European put option with strike price $100 are $10 and $4 respectively. The term-structure of interest rate is 10%. Is there any arbitrage opportunity? If yes, perform the arbitrage.